Yes tonsillitis can go away on it's own without any medicine or medical treatment.
Most cases of tonsillitis are caused by a virus just like the flu is caused by a virus and when the virus that caused your tonsillitis gets out of your body then the tonsillitis will usually go away on it's own.
You can help get rid of your tonsillitis at home by gargling salt water, drinking warm tea with honey, taking a spoonful of honey, eating popsicles or sucking on some ice etc.
Gargling with some apple cider vinegar or even drinking some apple cider vinegar in some warm tea or water can also help heal and get rid of your tonsillitis.
The tonsillitis should go away within a few weeks and if not you should see a doctor just in case you need antibiotics if it's a bacterial tonsillitis.