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

Tonsillitis. Tonsil pain, enlargement, with exudate (white patches), can be caused by viral infection, or bacterial infections. After cultures and blood tests medications are prescribed. Multiple severe or intractable episodes of tonsillitis may eventually need a tonsillectomy, or surgical removal of the tonsils, which would be done by a ear/nose/throat surgeon.
Yes. A general physician can certainly make the diagnosis of acute tonsillitis and treat you appropriately. Of course it would be nice if you have acute inflammation of the tonsils that a culture and sensitivity be performed to identify the cause of the problem.
Tonsilltis - Primary. Tonsillitis is a common infection of the upper airway and digestive tract. It is caused most of the time by a viral or bacterial infection. Typically, a rapid strep test is performed to look for strep throat. If this is positive, antibiotics are prescribed. If negative, usually symptomatic treatment with pain meds is sufficient. Your primary care provider can treat common tonsillitis.