Right side of face, jaw, teeth, gums hurt horribly. Plus, Coughing, sinus pain/pressure and headaches. Is this sinusitis? Happens 2 weeks at a time.

Possibly. Best to get a Dr to look at it, especially with the spread of symptoms you describe. Antibiotics might be in order.
2 separate problems. These 2 problems should be addressed separately. 1. swollen gums - can be a sign that you already have, gum disease or dental abscess. See your dentist. 2. Headache, sinus aches, coughing- seasonal flu is very common viral infection with symptoms you have described. Usually the condition resolves on its own with home care. Drink water, NSAIDs and get a good rest. NSAID. .
Can be . sinus,dental or both, so see doctor and dentist for an evaluation.
Very possible. Generalized dental pain secondary to sinusitis is very common. If decongestants make an immediate difference then its likely your sinuses. A tooth that has become a chronic problem can also refer pain elsewhere but the global issues and the cough are not usually associated with dental issues.