That stinks. I know that I had throat just as this was starting and it really worried me! Remember that there can be a lot of issues going on right now, regular old viruses and colds. If you have no fever or cough, I would just continue to shelter at home. Gargle with salt water, take acetaminophen and hydrate well. Get rest. I think the advice I've read a lot is that you should act 'as if' you have it to protect others. But it is doubtful that you do or if you do, this is just a mild case of it. I'd do what you can to minimize spreading it to anyone else (just as you would any other virus) and wash hands as often as you can or use hand sanitizer of 60% alcohol, wipe down what you can, etc. I personally would not risk leaving your home right now to test if you only have a sore throat. The places you go to test can be hotbeds in themselves. You are managing well it sounds.
Depending on where you are, it would probably be difficult to get a test for Covid-19 based on just a sore throat. Other viruses are circulating that give sore throats, and on lists of symptoms of Covid-19, the most common is a fever and after that a cough. Sore throat is not very high on the list. If you are in a country where it is easy to get tested, go ahead, but if not, they will probably tell you that you don't match the profile of Covid-19 and won't test you.