Ok, here's how I think it goes. For Future Trunk's timeline, Goku senses no one can beat Frieza, uses Instant Transmission to quickly get to Earth, and easily beats Frieza and his father King Cold (easily since it seems Goku & Future Trunks are at similar strength, and it was easy for Trunks). Since Goku mentioned he could've used I.T., I assume he would have in Trunk's timeline.
Now, yadda yadda Andriods etc, Trunks decides to travel back in time. This creates a new timeline, or he finds a new timeline, whatever - in any case he jumps into the version of the DBZ universe we've been following. He beats Frieza and Cold, and gives Goku the medicine. Goku mentioned he sensed a trenmendous power fighting Frieza, and hence chose not to use I.T. yet.
F. Trunk's original universe is still there waiting for him, and now there's also the universe we're following.