I Do know the first word but the second is lulabye!

there are too many L's

No.. its ME!!!

Lullabye!!!!!

It never looked right when I put it in the first place, Oh my!

Vaccinations almost matches the first word but has one less "i".

As to how you unscramble these words - the easiest way is to cheat !!!
Or you could say this is simply maximising the resources available to you.

Try one of the many anagram solver sites out there on the WWW.

I like The Universal Anagram Solver but there are many others.