I second the seat height suggestion. New cyclists often have it too low in order to be able to stay on the saddle with both feet on the ground. That robs you of power.
I second the up-your-cadence advice, too. Aim for a cadence that hurts neither your legs nor your breathing. IOW, aim for a cadence at which your legs start hurting just about when your breathing out as much as you can. Experiment on flats, if you have some. Sometimes, you'll just feel stronger at one cadence than another. At some points in the last couple of years, I've reached quantum leaps, when I find going to a higher gear gets me going faster ... which i assume is an effect of conditioning.
Keep riding, without criticizing your speed, cadence, ability/inability to get up a hill, etc. It takes riding more to be able to ride better. Just accept that starting in hilly country will make your progress seem slow - but at 33, you are likely to have more than 50 years in front of you, so you have time.
When I was younger, I used to push myself to go a little farther than I felt comfortable going. Then I hurt my back, and the only way I could ride for a whole season was to go a little less far than I thought I could.
I also second the HRM recommendation. In past years there were times I found myself just needing to stop for 10-15-20-30 minutes. I could breathe easily, and I felt no pain, but I just felt I had to stop. An HRM I started using this year showed me why: when my HR stayed above 140 for, say, 10 minutes, I could not recover without a long rest, often several rests. But as long as I stayed below 140, I could ride without long rest stops. Yesterday I was above 140 for most of an hour, took a 15 minute rest, and rode home in 1:05. (I'm old and slow, and my primary goal is to have fun riding.) IOW, if you keep riding, you'll improve your fitness.
How do you know your speed? If you have a 'puter, what kind?
In any case, the first time I rode a bike as an adult, I rode a mile ... and had to literally crawl upstairs when I came home. You're doing great!
Last edited by philbob57; 08-03-19 at 04:53 PM.