You will get better and more confident. Our stories are a bit similar. I turned 70 this past April. After 20 something years, I bought a bike last summer (end of June, early July). Around here, it's a mix of hills (steep ones) and flat but mostly hilly. The first month I started, after 5 to 8 miles, I'd had it. Now I'll do anywhere from 15 miles to 25 miles and I try to get out at least 3 days a week, more if possible. Some days seem easier than others but what gets to me the most and is often said around here, it isn't so much the heat but it's the humidity. Exercise and fitness are my main goals and the bonus is I have fun doing it... it's not like "geeze, I have to go exercise". Anyway, hang in there, if you keep at it, you'll gradually do longer rides and things will get easier.
One thing my wife and I enjoy are some of the near by Rail Trails in Ohio (we live in N. Ky.). Trains needed pretty flat ground to run on so those are nice and flat to ride on. Those rides we go at a leisurely pace which I call a "smell the roses" speed. Generally we'll do around 30 to 35 miles with those. We simply take in the scenery, take breaks when we want to and just simply enjoy the ride with no fitness goals on the agenda... although even slow pedaling there is fitness gains. So if you have any rail trails nearby give them a try.
Over the winter I didn't get to ride nearly as much as I wanted to in order to keep up the fitness gains I had made. I did end up getting a stationary bike which helped keep me ready for Spring. Nothing expensive but does have a LCD display where I can "ride" several different trails/areas... that and I have the news going on the TV. It isn't as much fun as really riding my bike but between the on screen trails and the TV going it does help make it seem a little bit less like being a job to do.