Can tonsillitis go away on its own without any further intervention?

Yes: If you have a viral infection involving the tonsillar tissue, it is certainly possible that your immune system can eradicate the virus in about 2 weeks. If the tonsillitis lasts for more than 2 to 3 weeks, culture and sensitivity of the tonsillar surface will tell us if it is a bacterial pathogen present and an appropriate antibiotic to use.