Are any special tests needed, or can a regular doctor see me for my rhinitis?

Rhinitis. It's a good idea to see your primary care doctor. Depending on what he thinks is causing the problem will determine what tests he does. If he thinks it is just run of the mill allergies he may order a steroid nasal spray or an antihistamine pill. If that doesn't do the trick he may decide to do testing to find out why. For example, allergy tests or a ct of the sinus.
Usually yes. Usually your regular doctor can treat your rhinitis, but they may consult with an allergist and/or an ear/nose/throat specialist.