Two dentists opinions toothache under bridge swollen gland hot cold sensitive.one said x-ray paper bite test no infection hard to see thin nerves may be sprained or fractured other said nerve exposed maybe sinus use desensitve paste will improvetrue?

Anytime there is sensitivity to hot and cold in a tooth ,it means the nerve is inflamed, or dying. Since you say no infection, the best you can do is have the bridge removed, or if a root canal is needed it can be done thru bridge or directly on tooth . If bridge removed than tooth can be worked on to save it from an extraction or root canal A cone beam x-ray would be of great help in planning

I am not a dentist so when I see a patient with tooth ache, temperature sensitivity with swollen glands (reactive lymph node) I usually make the diagnosis of tooth infection and treat empirically with a course of oral antibiotic. Those 2 conditions your dentists diagnose should not cause reactive lymph node by my limited dentistry knowledge.

Would recommend that you see a specialist Endodontist. Isolating and treating dental pain is what they are best trained and equipped to do. Nerves do not get sprained or fractured. Desensitizing toothpaste may help you have gum recession and root exposure, but will not address sinusitis. Please seek 2nd opinion from dental pain specialist.