I agree that you should see a cardiologist if you have a history of heart issues.

This being said, hills are THE hardest thing, for both running and cycling. It's where my fitness seems to leave me first when I don't exercise as intensely for a while. How experienced are you as a cyclist and as an athlete in general? How much have you trained before? If you've been doing this for years, you're hitting hills every other day and it feels the same all the time, then I'd recommend investigating your condition more. The good thing is that hills are also where fitness gains are the fastest and most noticeable.

I agree with Oakleaf's advice to mind your breathing. Also, try to take the hill as easily as possible, even if it's really, really slow, so slow in fact you might fall over You can go as slow as 5 kmh without falling if you have a triple. Focus on your breathing and heartrate, keeping everything under control. If it's not under control, go slower, or stop for a few seconds, then start again.

Good luck. And, yeah, see a cardiologist. Don't let your family doctor tell you not to worry about it, request a reference...