So I was wondering: are we allowed to use picrews as our avatars? If so, how would you go about crediting the original artist?

Yes, Picrew images are allowed on site, both in the forums and as avatars/banners provided the picrew follows the image rules and isn't fandom.

The best way to credit a picrew artist is to either state [Artist name here] on Picrew, or link directly to the picrew you used.