My LO started furiously sucking her hands at 4 weeks and has only started properly teething in the last 2 weeks at 5 months old and now I've seen that, I think that the teething symptoms are completely different.
My DD has always loved her hands, and in your case, I would say to let her get her hands in her mouth when she wants as she's exploring and learning and those motor skills are so important.
If Ava has dioreeha (sp?), rosy pink cheeks, is drooling and very gurney, then I would say it was more likely to be teething. Also the sucking DD does of her hands now is more chompy like, whereas before she just sucked them.
I hope that makes sense!
Valentine Xxx