Just make sure you have the recommended air pressure in them. The tires will squish some when you hit a rock or something like that. If your really concerned a lot about it, carry an extra tube with you as some added insurance. It never hurts to be prepared.
You seem like you scared/nervous since your just starting to ride again, and that normal. Just relax and take the bike out for a nice cruise through the neighborhood, through the city, or down a country road. It will all work out in the end. If you have a issue, take care of it and just keep on riding.