Hot sensation in gum and front fixed bridge with sort of itchy

I caught the cold past 3 days ago, and since yesterday I feel my gums hot and some inner itchy, and runs down to my fixed bridge. I am thinking that probably the cold has turned into sinusitis or some kind of viral infection which brings this sensation. I wash my teeth daily, and rinse them with water mixed with peroxide, every night before going to bed. Gums are not red, not swollen, they just feel hot inside and bridge as well feels hot, no pain to bite, eat, drink cold or hot. As additional information, the bridge is fixed with posts encrusted in my roots. My nose is still running oftenly, sneezes, my nasal walls burns bad when I cannot sneeze. Can somebody advice who to visit, Dentist or Ear Nose & Throat specialistDoctor? If I can get a home remedy, I will appreciate.

Thank you very much :-)