65 is normal, a little on the low side but if you exercise regularly this is normal, so don't worry about it.
You should go to a doctor and get checked out, but you may have something called reflux which is the most common cause of chest pains. If you eat a lot of acidic foods this is very likely to be the case, although it can still happen even if you don't think your diet could be a cause.
If you go to a doctor they will send you for an ECG to rule out any underlying heart condition. If there is nothing they will do something called a pH probe- this is a tube that goes up your nose and into your esophagus
for 24 hours- it is not painful, just uncomfortable, and you will have to stay in hospital. If this is confirmed you will be put on a medication such as Omeprazole
for about a month, which is nothing to worry about because it is very safe.
It is only in confusing cases that the doctor will send you for a pH probe- he may be able to diagnose you without it.
I had this for a short while last year (I'm 15) and it was fine- I didn't have a pH probe and I was on the medication for a month and it went away.
I had the pH probe done another time when I was in hospital for some respiratory problems, and it's a weird feeling but nothing to worry about if that's what does happen.
Hope this helped, best of luck with everything.