My daughter is the same age as your little girl, she's also 3 1/2 months and she has all the same symptoms as you mention. Yes, as far as i have been told, these are signs of teething, and it can happen this young! My daughter soaks her tops from dribble all the time and is forever trying to squish her whole hand in her mouth or at least a few fingers (which has resulted in lots of gagging noises! She still hasn't learnt) Babies can get teeth at any age! Me and my 3 brothers and sisters all had two teeth at 12weeks and some babies have been known to be born with a tooth or two, whilst some don't get them until they are almost one. They will come through eventually and i guess if they are not causing her too much discomfort?? or are they?? They will come through in due time. GP said to to me, that they might also just be moving around her mouth and can easily go down and come up properly.
Hope everything is going otherwise. I got a teething gel from the womens and kids hospital (i live in adelaide) that works wonders on her swollen sore red gums when they are bad. Be careful if u want to use teething gels as many of them have age limits on them, usually at least 4-6mnths. I use baby panadol at night times occasionally if she is really unsettled too.
Hope this helps
DD#1 - 3.7yrs, DD#2 -20mnths, DD#3 is here! 21.08.