for 1 handed I used shadowmere but with 2 handed shadowmere takes damage but 2 handed doesn't raise any. Any suggestions.

Use it all the time in combat.

It really is just the best way to level most skills. However, some skills are easier to grind than others, or have special exploits that can be used. But for 2-handed, as far as I know, just use it constantly.

Beat the crap outta the guy in the intro, before the sleeping bear.