Ok, first thing? An hour and 20 minutes should be sufficient time, even if you have a slight delay on the first leg of the flight, to make your connection.

However, worst case happens and you don't get to the airport in time for the connecting flight, yes, go to the counter. They'll help you adjust your travel plans. That's what they're there for, and they're used to it. If all flights are already booked, you can go standby, or they may offer to put you up in a hotel for the night.

Luggage? If it's checked in at the originating point to go all the way through (i.e. you're not picking it up at the transfer point because you're changing airlines or some such), it'll probably be put on the next available flight to your end destination, and will be waiting for you on arrival. So pack a change of clothes and all essential items (medicines and such) in your carry-on bag. Also, remember to only pack sample size toiletries in your carry-on, and have them in a ziploc bag. Check with your airline to see what other security restrictions they may have in place as well.

Now, relax and stop worrying. *g* Thousands of people reach their destination on time every day. You will, too.