Is there a way to select another one of my existing balls?
Unfortunately, there is no way to do that. Over the years, there have been numerous threads on this. So, it's not going to change. The only thing to do is to double-check your ball count before starting a round.
If you're down to a single ball, you might want to consider purchasing a sleeve before the start of the round. At a minimum, if it were me, I would first start a practice round so I could see how many hits were left if I only had 1 ball of the ball I was going to play.
If I had plenty of hits left, I'd probably just play the round. If it appeared there were only a few hits left, I'd purchase a sleeve before beginning the round.