Okay, well I'm not a doctor, but...
1. There will be individual variation in terms of how well people tolerate beta blockers and running (some people don't seem to have a problem);
2. I run seriously. I have high blood pressure. I was told to take Atenolol. I was on the lowest dose - because I'd mentioned the running - but it still completely ruined my ability to run. It was like having a tight band around my chest.
3. I saw a cardiologist (for my palps). He noticed the high BP. He said that he wouldn't recommend that I take beta blockers, because it would compromise my ability to run. (He suggested that I might try ACE inhibitors instead.)
4. But what you're describing sounds much more like the sort of gastric disturbance lots of people experience when they're running. If you've had cardiac examinations, and they were clear, if you're not experiencing crushing pain, or abnormal shortness of breath, etc., then the chances of it being a "heart problem" are vanishingly unlikely.
But I'm not a doctor, so...
ps., Obviously, you should never discontinue taking a medication just because of what somebody on an internet forum has said (whoever they might be, etc). Always consult with your primary care provider, etc (of course, I'm sure you already know this!).