HUGS. It is hard when they start day care. I was in a similar situation a while back. I went in to the nursery and demonstrated how to get my lo off to sleep, and talked a lot to them about sleep (even gave them some bw handouts, I was that obsessed!!). It sounds as though you are both doing really well. I think if she is not fussing at nap time I wouldn't worry too much and putting her to sleep early to compensate is a good idea. As long as the nursery understand her routine and the things you do when getting her to sleep and follow this, I wouldn't worry.
I think if she has molars coming & is upset, then I'd give her some medicine like you say, or give it to the nursery to use if necessary (difficult if she only let's you know she is in pain). The other thing I would do is to start talking to her. I know she is still very young, but talk to her about how it is OK to let other people (including named worker at nursery) know if she is hurting/ teeth hurt , by saying something (give her the words), so that they will help her or you could teach her the sign for pain and encourage her to communicate this.
Hang in there, it will get easier in time.