Hello. Ive been playing guitar for seven years and have just recently started getting into metal and fusion. I want to be able to improve my speed with shredding and sweeping to learn songs in these genres, and hopefully be able to put these techniques into improvising. Ive been trying to learn the intro to cliffs of dover for a while now but cant bring it up to the actual speed of the song. What i've noticed is that when i pick fast, parts of my right hand constantly rub against the other strings. I think it's causing friction when i play, and slows down my picking. It also gets annoying because it irritates my hand after a while. Im pretty sure i'm holding the pick correctly. Is this normal, or am i doing something wrong? Not sure if it makes a difference but my hands are a little smaller than average.
A video of yourself playing would be the best way we could analyse whether or not you're doing something wrong. I could write a big essay on different things to do, but if you want the best advice you should post a short video
How are your mechanics for doing what you want to do?

What you are looking for takes certain skills to accomplish and the best book on that subject are speed mechanics by Troy Stetina that will cover all you need. Its the shred bible for many guitar players.