Can gingavitis hurt like a cavity or know somethimes my pain moves side to side I was told at ER my gums were swollen going to denist today?

Yes. This can very easily cause pain in mouth as referred from a tooth etc. Please see dentist may need plaque buildup removed and also need antibiotics perhaps?
Usually not. Gingivitis usually does not "hurt" though it is possible if you are having a particularly large flare up in a specific area. As with any inflammatory disease discomfort may be a source of a dull and continual ache.