I'd go to a doctor first to query if there may be any heart conditions/etc that you may have first.
Otherwise, no, I do not suggest you stop working out, it is an essential part to your well being, the benefits you get from it isn't something you can really substitute from other sources. Even if you have a very good diet, etc, it will not be sufficient in maintaining your strength over the years. Having a great diet for all your life, for instance, will not take care of the issue of not being able to pick up your grand kids when you are 70.
By the way, how far did you try these cardio exercises? Did you end up panicking and quitting within the first few minutes as a result of the jump in your heart beat? You should know that for when you are doing a cardio exercise, that your heart rate will spike up for the first 3ish (this number obviously varies within the individual) minutes before reaching a steady state. So if you have quit early ahead whenever you attempted because you were worried, as long as there was no pain or discomfort during this period, I would suggest trying to continue to exercise for at least 5-10 minutes and see if your heart beat reaches this steady state.