That part will come with time. There are a few things that could be contributing. One of the obvious is hand strength, you are using muscles you haven't used before. Secondly, check the action of the guitar. Action is what is referred to as the height of the string off the fretboard. The higher the action, the harder it will be to press down basically. Try to lower the action, not too low or the intonation may get out of whack or your strings may buzz. Your local guitar shop should be able to help for a relatively cheap price. Also make sure that your thumb is lined up with your barred finger. Work on that press. Don't do it too long or that little muscle between your thumb and forefinger may cramp up.

One more thing that could contribute. Wearing your guitar too low. Raise the strap up an inch or two. That will help your hand to be able to be in a better position and not have to bend your wrist so much to get in position. Think more Tom Morello and less Larry Lalonde

Do not "fret", I have been playing for 21 years and it still happens to me sometimes when I am playing an acoustic guitar with high action.

Keep at it. Practice REALLY does help. learn your basic chords then try to teach yourself songs to keep it interesting. I find that Nirvana has a lot of beginner friendly songs.