Wow. Life has changed in the last few weeks, and it's kind of scary, huh?
I think step one is to call the teacher. Find out how she is doing in school, if she seems comfortable, if she's making friends and fitting in, or if there are problems there. I found that my kids were fine out in public, and the horrible behavior always happened at home, when they felt safe. But first be sure behavior at school is okay, and if you want to, get permission to attend a day of school to see for yourself. Your presence will change everything at school, but you should have a right to do that. (It's just tough around working)
It sounds to me as if she's a little taxed right now. she can hold it together, and probably does at school, but it gets to her when she finds something she does NOT want to do at home. Probably at school there are things she HAS to do that she doesn't want to do, and she can't act out there.
Maybe you could try debriefing the day when you get home from work. On the way home from daycare, tell her to tell you about her day. First you got to school, and found your desk, then what ? Who did you play with at recess? Did you run around ? Swing? Think of as many questions as you can that will get her talking about her day. Then you might find out what's going on that has her tied in knots.
And along with that, I might think about moving bedtime a little earlier. That way you can sit quietly together and read a book, relax and cuddle and then tuck her in before she's totally exhausted.
If nothing works, then, yes, definately talk to your doctor. and try to talk to the doctor on the phone BEFORE you bring your child in. That's hard these days, but you probably want to say things that you don't want to say in front of your child. :-)
Good luck. Parenthood isn't for the feeble, is it ? And sometimes, don't we feel feeble, and don't we wish someone else could simply solve the problem ? It's a whole lot easier to be me and toss some ideas out than it is to be you and try to cope night after night and wonder if your child is okay. I feel for you.