Look at a capo. The part that pushes on the back of the neck is your thumb. The rubber part that pushes down on the strings is your barre finger.
Take your basic Am or any other open position chord...... E, Em, E7, Em7, Am, A, Am7, A7 etc
So normally you would play an Am triad like this right......?
Now play it like this............notice that now your first finger is free.
Now, keeping those fingers on the strings, slide them all up up one fret, while keeping them grouped like before....all you are doing is sliding them all up one fret. Now flop your 1st finger down across all the strings. Now play it and you have a new chord....a Bb minor. Slide the whole thing up one more fret....this is B minor.......one more fret this is C minor.
Do this with your open E and E minor shapes, and also with the open A shape. Fret the chords so the first finger is free.......so you can slide up and barre it. Get into a habit of playing them this way at least 1/2 the time, whether you need to or not.
Also, you need to develop a bit of a callus on the fretting edge of the 1st finger on your fretting hand. Practice just fretting across the whole finger board at different frets up and down the neck.....no chord, just fret it and play the fretted notes across the strings.....make them ring, no dead one's. If there are dead one's you need to analyze why that is happening. Maybe you need to bend the finger.......either more straight or less straight, find it's happy spot.
Try sliding your barred finger up and down a couple few times each time you practice to strengthen that callus. Careful at first, baby steps.......don't cut yourself.
So, moving on to augment that idea of developing the strength in the barre finger........Once you can fret a barre cleanly.......try add notes. Start with one only.
Example: Say you have barred across the 3rd fret. Now add your 3rd finger, 5th fret, 5th string. This is
G minor 7th.
Now add 4th finger, 5th fret, 4th string........
G minor
Now add your 2nd finger 4th fret, 3rd string......
G Major
Now holding that....lift off your 4th finger on the 5th fret, 4th string...... this is
G7th.
Remember this goes for all the fret positions.....sliding any of those chords up or down, just changes it to a different root, after which it is named...but it's the same chord. In the case of the open E shape family, the root is the note on the 6th string. In the open A family, the root is the note on the 5th string. So the chord on the 3rd fret we just did....it is from that open E family, the barre finger is on the 3rd fret....that note is G....so the root is G. With that A minor chord, if you slid it up to the 5th fret...the note on the 5th string would be a D, so the root would be D.
Practice playing all your open chords with the different fingering I suggested. It will get you really familiar and comfortable with it. This way if you are playing a song and a barre chord is coming, when it gets there just fret the 3 fingers correctly.......play just those notes, while you get your barre finger down and secure. You are only looking at a fraction of a second but it will buy you some time, a short amount of time to fret the barre correctly and then play all the notes or slam the 5ths or whatever, pick out an arpeggio etc etc.
Good luck!