One of two things are wrong.
1.) You have too much tension on the cable. To check the cable for stretch wear and properly evaluate the front derailleur mechanism, you need to shift it down into the lowest gear/smallest cog. Unfasten the cable, pull it tight with your hand to remove all possible slack, and while doing that re-fasten the cable to the front derailleur bolt. If you cannot ascend the gears cleanly, this will tell you that maybe the cable has stretched too much and needs to be replaced, or the spring in the front derailleur has worn out its life and the entire unit needs to be replaced.
2.) You have too much leverage applied by the high limit screw. Peek inside the derailleur and check the high limit screws descent. Unwind it a touch, and then try again. Do not force the gear because you can break the shifter. If it does not cleanly ascend, unwind it a little more and repeat to troubleshoot. Another method involves unwinding it all the way, shifting into the 3rd cog, then slowly screwing it back in until you put just a little torque pressure on the lever hammer with the screw. Shift it back down and up again to check it's working properly.
If you're getting chain rub, then you need to check the alignment of the derailleur on your seat tube. The outer line of the cage needs to be running linear to the chainring and should be positioned about 3mm vertical (above) and lateral (to the side).
A third possible element is you broke your shifter mechanism and it needs to be replaced. You can unlink the cable take off the cover and check inside. If it doesn't click all the way from freestance, then it means the mechanism is broken.