YW. You might be using too high a gear, so pushing too hard, which will
definitely slow you down going uphills.
In general for reasonably flat riding, you want to be spinning at 80-90RPM. Most cyclists I see are spinning much slower, so pushing much harder. Think in terms of lifting a weight. You might be able to lift 10kg only six times on some motion, but you can likely lift 1kg far more than 60 times with the same motion.
I also have a lesson from Mt Washington. I was an unranked teenage amateur bicycle racer doing ok, but only using bicycle racing as training for ski racing. I'd won a couple regional-level hillclimbs and was looking for another race and someone said "call this guy". I did, and got told about the first Mt Washington bike race. I had no idea what gearing to use, so got the lowest granny-geal cluster I could find in a day. I got to the race and among the small crowd were four guys from the US Cycling Team. I wound up finishing 3rd, only 4min behind John Allis (3-time Olympian) 1h:15m time and 4sec behind 2nd place. I had by mostly dumb luck out-guessed everyone on the gears (neither my conditioning nor my bike was close to their class). The next year Allis came back and won again knocking 14min off his time, presumably with a lower gear cluster.
So, I'd definitely take a look and see about using lower gears...