Rachel, there's no need to panic. Your rear tire is good for quite a few more miles. But you could do yourself a favor and buy two road tires of that size. Then either splurge and put both on or put your current front in back and put the new one on the front. (When the rear goes, the newish road front goes in back and your other new road tire goes in front.)

If you do the first option you won't see a huge change. Replace both and the bike will feel quite different and it will be fun! (The rear tire is the key to a better feeling ride.)

Again, what you have now is perfectly safe and ridable. New road specific tires with much smoother thread will however be a big step up for a nicer ride.

Now a question: Do you know how to change a tire and tube? Have you done it yet? Flats happen. Flats have been happening this past 130 years and will for probably the next 100. You will see one. Being prepared is the difference between a not so fun, dirty hands ride and possible an epic experience you never want to see again this lifetime. Changing tires and tubes isn't hard - if you have the right tools and know what you are doing. A bike shop can show you how. If you have them swap the tires, ask them to do it in front of you. But beware. Watching someone else helps a lot but you are not there until you do it yourself. If you have a bike coop nearby, I highly recommend riding there and taking the tire off and putting it back on yourself with them around to show you the tricks.

Rachel, I've been following your journey into cycling since you first came on board here and refrained from saying anything to not scare you off. You're a trooper. Troopers fix their own tires. It gives them a big step more freedom. (And if you already know and can do this stuff, congratulations!)

Ben