I'm just the opposite with big hands and fat fingers. Still I had/have the same problems with nailing the strings and notes. It is just a matter of keep adjusting your hands until you find the sweet spot for lack of a better term. I did have a better set of strings put on my guitar and the bridge lowered, these two things made a big different with my guitar. With this work done (cost 26 dollars) I was able to play the F Major right away. Still have to work on it when I’m running throw my cords, I’m a beginner like you. I went to the music store and got a Gripmaster Hand Strengthener.