I know exactly what you are talking about with the F chord. It is really different feel. I taught myself the guitar - incorrectly about 20 years ago and am not starting all over to learn correctly. However, for your problem, the way I solved it was to put my index finger on the bottome two strings, B and E, as if I were going to finger an F chord. Just keep the bar on those to strings and strum them by themselves until you get a good clear sound. Keep doing this over and over and slowly beging to add the other fingers. I promise, this will work. The F chord is really difficult in the beginning, but it is a must for many songs so the work is worth it. Hope this helps.
Ralph