No matter what size your hands are, they manufacture a guitar that will fit your needs. You can also resort to tuning down 1/2 step or switching to nylon strings to relieve some pressure when training your hand to form what seems to be difficult now. It will come, I promise, just keep focusing on your progress and soon barring will become natural when you need it. Some of the greatest sounding chords are played between the 5th and 12th frets up the neck and require some form of Barre method to attain (or deaden) the notes.
I encourage you to practice barring those chords and the results will shine through your playing;;; Barre None...........................
Good luck...