The rules for New Mexico are here http://www.bon.state.nm.us/cont_ed.php
Apparently NM requires 30 hours every 24 months. I don't see if they make an exception for the first period of licensure, so you may have to cram in a few courses really quick to maintain your standing.
You can find NMNA approved CNE activities here http://www.nmna.org/default.asp?PageID=10005583
is on the list and has free courses...
is also on the list. I did not see rn.com, but they may be ok, you will have to verify that with NMNA, possible since they are ANCC accredited.
If you can't come up with the credits, you may be able to go Inactive for a period until you can catch up which will be infinitely better than letting your license expire.
I am not from either state, and have no relevant experience with either BON or organizations in these two states, so I can only offer this general information.
Hopefully someone from NM and/or AZ will see your post and be able to give you more informed and focused guidance.