Testing does need to keep expanding given the scale of it. The quicker tests should help some. And from what I have heard the tests are much more widely available now, as opposed to initially. Working through back logs will take some time though. But testing is critical particularly for those exposed the most, even if they are not showing symptoms.
I understand your fears and this is going to be the lamest thing to say, or among them, but have you talked it out with your family? I know it is hard and I am sure that there are various fears that everybody is holding onto. Sometimes that can help, knowing that they are there and you do not have to carry the load alone or that they do not need to either.
Everybody is scared and worried. If not for ourselves than for our loved ones. And there is nothing wrong with that. And again, easier said than done, but there is no sense worrying about things we have no control over. Emotions rarely have sense though.