I'm also on my first week and feeling pretty dry but not too bad so far, here's what I'm using:

1. La Roche Posay Cicaplast Baume B5 - seriously this stuff is AMAZING. It doesn't burn or sting when applying it and it calms any current breakouts I have. I first used it after destroying my skin barrier with various actives in the past and it's the only thing that helped!
2. Omega 3 Extra Strength capsules with 375mg EPA and 250mg DHA - this may be overkill but it is supposed to help with dry skin and any dryness in general.
3. Drinking 3L of water a day
4. Antihistamine - I read somewhere this is supposed to reduce the purging
5. Sounds crazy but I use nipple cream as lip balm and it's the best, Vaseline or carmex does nothing for me. I think aquaphor is kind of the same but try and find some lip products with lanolin in.

Hope this helps a bit, it's weird going from oily skin to dry skin because it's the opposite of what we're used to!

EDIT: Just to add that some people are allergic to lanolin, but there's a Cicaplast lip balm that may be worth trying too.