I'm also a bit confused as to whether you mean your skin or your lather drying out, but as the latter is probably the more likely, you perhaps have too much cream in the lather? Should be like the consistency of egg whites when you beat them to make mirangue (at least that's how I like it).

As for the pulling, I remember my first few shaves felt like I was scraping myself, so it might just be a matter of your face adjusting to a new sensation. Alternatively, a razor that pulls is usually a sign that it's not sharp enough and may need a hone.

James.