Vomiting is not a sign of teething. Pain will cause diarrhea and so will pain meds, but not vomiting. Vomiting is a sign of infection, food poisoning or food intolerance. I would also question the runny nose esp since all of these signs (including the runny nose) are signs of the rotavirus--a nasty stomach bug. (do a search on it for more details).
My son had the rotavirus, and another sign of it is the horrible putrid smell of the diarhea....so if all of these are present, I would bring him to the Dr.
He could be teething AND have a bug though.
Baby Motrin will help with any fever and teething.
Besides that, you are doing the right thing by keeping him hydrated since dehydration is the number one problem cause by a stomach bug.
I would also limit what you are feeding him to the brat diet, which at 7 months would be baby bananas, apples and rice cereal. And if the symptoms last more that 48 hours--go to the Dr.