Hi, I have just a couple of words for you: alternate picking...

If you watch this girl's video closely (yeah, she rocks big time) you'll see that on the really fast passages she's doing it.

Other than that, while you progress with your downpicking technique I'd suggest that you try something easier than Metallica trash songs. I don't know how long you've been playing but I know for sure Hammett wasn't born playin´ MOP :P
Patience...

I may also recommend that you do some muscle stretching before and after playing. It will help you avoid extra tension and prevent damages on your health.