Teething at 10 weeks??

My LO is 10 weeks old and has been gnawing on her hands, hasn't been sleeping well, has been drooling a lot causing her chin to be so chapped, and now today is pooping a ton and her temp is 99.4. She's also had a little bit of congestion. I know the pooping isn't a tell tale sign and all the other symptoms really could be anything but I'm wondering if she's teething...or maybe getting sick? I feel like 10 weeks old is way too soon to be teething!