You'll be surprised how little force you'll be using later on versus what you're using now. Things will get more and more efficient as your technique improves. But until then, someone else here suggested rolling your barre finger back a bit so you're fretting the barre more with the side of your finger. That's good advice as the side of your finger is a bit bonier, and the strings can't get lost in the creases at your finger joints as easily. Another thing that helps is instead of squeezing so much with your hand, pull back on the neck with your whole arm and use some of those larger muscle groups to apply pressure to the fretboard. Some people use a sort of downward version of that where you use the weight of your arm to add pressure in a down and back direction.

One thing to keep in mind which may help is that you don't need to hold your barre across all six strings. Your other fingers are covering the A, D, and G strings, so you only need to focus your barre on the E, B, and e strings. And when all else fails you can consult Uncle Ben .