[Lavaere]

I don't know how your doing this but each skill should have its own experiance chart. Start learn sword, gain enough experience and your sword would go up a level.

Self training this is going to take a long long time. But if you have a tutor it will be easier and your able to train up to what ever his level is. You want to be better then him, start some self training.

Now for schools of fighting. You would have prerequisites for learning them. First of all you need to join that school, or find a teacher to tutor you. Another prerequisite would be other skill levels.
Say you want to learn Franz Swordmanship(or what ever you want to call it) which is a dual fighting style of sword with dagger you might need level of Sword 3, Dagger 2 and Ettiquette 1. Before you can even start Franz Swordmanship. And because its a specialise fighting style it would have bonuses when using it.
And depending on the School it might teach you the prerequisite schools as well. Or perhaps you will need to go somewhere else to learn something.
Franz School teachs up to Sword 6, Franz Sword 3, Dagger 2. Meaning you would need to learn Ettiquette somewhere else before you can start on the Franz Sword skill.

You could even have other things restricting you like needing to sponsered by someone from that school. Or needing to beat someone or win a tournament before they will let you advance furthur in that school.