Get a scramble, save it and then solve it slowly without timing it. Pay close attention to what you're doing, and memorize the solve. As in, memorize the cross and just go over the F2L a few times to not really have to look ahead anymore. Remember the OLL and PLL you get. Then, do the scramble as fast as you can to a point where you're turning at your max speed without pausing at all. If you cannot get faster than your current speed, then maybe your hands are too small, maybe it's something else. Realistically you could probably get sub-10 on a practiced solve with small hands. Just do this once to get it through to yourself that your hands are not a problem. Don't make a habit of it.
(If you don't do CFOP just adapt what I said to your method, of course)