Not getting better is one way to tell. Also it can depend on what other sorts of symptoms you had when it started etc. I think the dr either has a look (sometimes they can see redness or pus) or listens to the story and makes a judgement call.

Gargling with 1/2-1 teaspoon of salt in warmish water 3 or 4 times a day can help. So can warm tea/herbal/hot water with manuka honey in it. Also, strangely enough, sometimes the problem is with your sinus area, so if it's sore a bit higher up, then saline nasal sprays/rinses can help.