It is a perfectly normal milestone that she has reached called mouthing. At her age babies start putting EVERYTHING in their mouths, I used to say that Brandon did not know what it looked like until he had had a good taste, lick and a nibble of whatever was in his hand.
But for drooling you can try a Baltic Amber Teething necklace, these reduce drooling drastically and help with imflamation later on when she does start teething, otherwise there is not much you can really do except put a plastic backed bib on her and a bit of vaseline on her chin to help prevent a dribble rash.
As for helping with the pain of teething, TeeGel did the job for Brandon, but nothing for Liam - all that workd for him was Prodol.
But try avoid medicating unless necessary as their bodies do build up a resistance to it.
For itchy gums you can try cold teething rings, rough textured toys, and when she is a bit older, baby biltong and ice lollies. You also get a textured dummy which worked with Liam, but Brandon hated them, so you need to see what your child likes / dislikes.