It's also worth noting that I am operating under the POV that Trunks was the one who killed Freeza and Cold in future Cell's timeline, not Goku, based on this panel of the manga:
Cell is explaining how he got the Z warriors cells and it shows Freeza and Cold being killed by Trunks and in a similar fashion happened in the main timeline (I'll call the timeline we are more familiar with of "main" timeline and the 1st timeline [the one which originated everything else] of original timeline).
You could argue that AT just recycled the art in that panel, but I don't think such explanation is necessary. Whilst possible (considering AT recycled the panels of Vegeta being defeated on Earth as well as Piccolo being defeated in Cell's very explanation, as well as recycling some panels in the Boo saga, where we have even Kuririn making a joke and a Tori-bot appearing saying the editor shall not pay him), I don't think it'a a need to think so in this case. Sure, it'd obviously raise the following question: "shouldn't Goku have survived then? Because Trunks would have obviously handed him the medicine."
But the truth is that Goku could have died from other ways besides the heart disease... it's very possible he was assassinated by the androids much like the other warriors. Sure, he wasn't killed by the androids in the main timeline, he survived and trained in the RoSaT... but you have to remember that there was an important being influencing what was happening in the main timeline: Cell! Yeah, that's right, the fact that Cell travelled to the main timeline hugely influenced its happenings, and it might have even changed the time where Goku got ill. It's possible that in future Cell's timeline, without there being a Cell there influencing what occurred, Goku also got ill not too long after Freeza's defeat... and then he was just fine when the androids appeared and would have, along the other Warriors, have confronted them... and then was killed by them.
What is interesting is that it would imply that Goku being saved by the medicine didn't help in saving the world... much like in future Trunks' timeline, the world was also doomed even when Goku got the medicine... and the direct responsible for the World's salvation (yeah, that's right, guys!) was Cell! Yeah, considering that in Cell's timeline where Goku got the medicine the World was still destroyed by them killing machines, the one altering what happened and then saving the World would be Cell also traveling to the time line and changing its happenings.
Then, that's what happens, from my POV (notice that I am not arguing that Freeza being killed by Trunks in Cell's timeline is a fact, and am perfectly well if you disagree, but I think it makes sense):
Saiyajin Goku wrote:History A1 - Son Goku returns to Earth and defeats Freeza and Cold. The Saiyajin then dies of a heart disease and the androids # 17 and # 18 dominate the events of A1, forcing Trunks A1 to travel to the past (pretty much a parallel of Mirai Trunks' timeline). The rest of the events are unknown.
Past Alternative A2 - Trunks of the future A1 defeats Freeza and cold. However this is still not enough to prevent Son Goku's death, the androids sow the destruction, but due to unknown events they are somehow disabled (some people saynit's due to a remote control). Pass 23 years from the incubation of Cell A2 and he starts his search for the androids. The A2 Trunks decides to travel to the past to change the events, however chooses 1 year before the arrival of Freeza and Cold for whatever reason. With no knowledge that there was a third android (Cell), the Trunks A2 is defeated easily by Cell A2 and this latter returns to the past to attain his perfect form. In this example the Cell A2 will travel to the past alternative B2 (explained below).
History B1 - Son Goku returns to Earth and defeats Freeza and cold. The Saiyajin dies of a heart disease and the androids #17 and #18 dominate the events until Trunks B1 travels to the past. With his return after the triumph in the past B2, the trunks B1 destroys the androids #17 and #18 and years later defeats the Cell B1, preventing him from returning to the past. In this line of events the Cell B1 is aware of the existence of Trunks B1, but the data itself is unknown.
Past alternative B2 - the Cell A2 travels to the past without being aware of the parameters of the journey and reaches this new past 1 year before the arrival of Trunks B1. Then, it happens the history portrayed in the manga, the Cell B2 is destroyed while still in larva, the Cell A2 reaches his perfect form and is defeated by Son Gohan in the Cell Games. The past alternative B2 is saved and Trunks B1 returns to his time and saves it as well.
Also, it's worth noting that, in the future Cell's timeline, Goku probably didn't die from a heart virus (considering that the future Trunks who came from yet another timeline should have obviously handed him the medicine)... he likely died because of the androids, so as far as the Trunks from Future Cell's timeline knows, Goku wouldn't be this game-changer as it was portrayed by Bulma in Future Trunks' timeline (as well as in the timeline of the future Trunks who went to future Celk's timeline)... so that could explain why that Trunks from Cell's timeline didn't try to travel to the past until he had already killed the androids... he didn't travel to the past to hand Goku the medicine, as the Goku from his timeline dies in another way. So the Trunks from Cell's timeline obviously perceived Goku in a different way compared to the aforementioned Trunkss.
Moreover, there isn't a need to have a timeline to where the Trunks from future Cell's timeline travelled to... that isn't hinted at the manga, and he could very well have destroyed the androids from his time without having to resort to traveling back in time... maybe the Trunks from Cell's timeline also found the scripts in the underground laboratory somehow, dunno.
Furthermore, Future Cell (from Past Alternative A2) would be the direct responsible for the creation of both the main timeline (Past Alternative B2) as well as Mirai Trunks' timeline (History B1) by traveling to the past of his timeline, so there would be a Trunks killing Freeza much like in his own timeline and this Trunks that killed Freeza (the past version of the Trunks that killed Freeza on his own timeline) would need his own timeline as well... to think of it in another way, if Trunks had traveled to the past a minute into the past while waiting for Freeza, he'd have found a clone of himself a minute away from doing the same thing, to which he'd have created two timelines because his time clone also needs his own timeline (that analogy was actually made by metal4ever).
But the problem that it may rise is that Cell should have altered the timeline up to the poin he traveled back, yet there's still a "Freeza being killed by Trunks" much like in Cell's timeline... well, we may then think that Freeza's death by Trunks' hands was still not altered by Cell, for whatever reason.
Amyway, I think this won't be so welcomed since most people might think Goku was the one who killed Freeza on Cell's timeline, but oh well.
