M.B.
Hi J.
Yes you are partly right, symptoms such as runny nose and wet coughs are part of teething but if there are fevers thats generally means there is an infection and her body is trying to fight it. So tylenol is good to use for that. Sneezing since birth is a babys way of getting everything out because they cannot blow their nose.
I have a six month old and she has a bottle after she eats baby food/cereal also so I believe that is fine. But I would just ask your pediatrician and if she is not gaining too much weight then I would not worry about it. I hope I helped.