I wish I knew at the time that a good amount of pressure should come from pulling back at the shoulder of the fretting arm, bracing the guitar body with your strumming arm chicken wing. You can practice this by fretting the F without your thumb on the back.

Also, you could try to play the A barre chord at the 5th fret with the same shape as the F barre on the first fret. Will help build some strength

If your nut is a bit high, try putting a capo on the first fret and play everything the same, but a key lower.

Also advice from Marty Schwartz is to stop avoiding songs with F. Just play them with a poor F. They will start to clear up. F is hard to practice on its own because you use too much pressure at first and it tires your hand out quickly.

You’ll get stronger and more efficient with practice. Keep it up!

The slight roll to your finger that others have mentioned sounds like pretty good advice to me. I’d also try playing songs that you are already comfortable with in a barred position. For example, playing a classic I-IV-V progression (like G, C, & D or A, D, & E) at the 3rd and 5th fret. There is much less resistance at that part of the neck, and it pulls your hand in closer which can straighten our the muscles in your arm a bit if you have a smaller frame; this makes for less stress for your muscles across your list and the base of your thumb. So, while you develop the technique with less factors fighting against you, you can focus just on that technique, and not on learning a new song, or really feeling like you are having to work on something completely new - just different - which can make for a better mindset as well.

Your action is likely really high if you find you need to apply a lot of force. You can always practice barre chords higher on the neck too. There’s less resistance higher up.