I've read that dizziness can be one of the symptoms for Covid. The fact that your flu test was negative also makes it more likely that it is Covid.
The good news is that if you've already had it for almost a week and you haven't been hospitalized, maybe it's less likely that you will be.
Are you expecting the results of your Covid test by Sunday?
I'm not sure if your doctor needs to know about the symptom of dizziness or not, but maybe.