First of all let's eliminate you as the problem. Upshifting the front requires easing up on the pedals to near zero force. That's because chain tension pulls the chain down so you're fighting it if you try to upshift under load. When ready to upshift, keep pedaling but at zero force, just keep turning the pedals.

So try riding that way a while and see if all is OK. If not, it's time to adjust the FD.

1- set the inner and outer limits as follows. Shift the front to the inner. Check that the FD cable is slack, then shift the rear to the inner and (if necessary) adjust the inner limit so the inside cage plate just clears the chain. (odds are this is OK already).
2- set the outer limit. Leave the lever in low, and shift the FD by pulling the cable away from the frame. Loosen the outer limit trial and error, until you;re able to dump the chain over the outside of the large chain ring. No bring the limit back in by degrees until you 100% reliable cannot dump the chain, no matter how hard you try (still by pulling the cable directly)
3- Now, that the inner and outer limits are properly set, adjust shifting and trim via the cable. This is much easier if you have an inline barrel adjuster, but maybe it's already OK. The right adjustment allows crisp up and down shifts, and trims the cage on the outer ring so the outer plate just clears the chain in high.
4- It's possible that downshifting may be a bit sluggish, so feel free to back off the inner limit bit, but do not adjust the outer limit.