I’ve just started to have a cough that won’t go away… Even though you have been vaccinated, it doesn’t mean you still can’t catch Covid, but the effects are far less severe. You also can still catch the regular flu, even if you’ve had a flu shot, but it won’t be as severe. There still is no protection against the common cold either. I’d try to stay away from people until you find what the problem is. The first thing I would consider would be a Covid test. There should be places open yet tomorrow, Saturday, where you could have this done. Of course that can also be done at a hospital at any time.