Heart
murmurs are mostly due to abnormalities/disturbance of blood flow within the heart and vessels. Most are benign, normal variations in the structure of the heart and cause no problems. A murmur can be caused by problems with the heart valves, by holes between the pumping chambers, or just by turbulence in the blood flow- which is generally not a problem.
It really depends on the cause of your heart murmur; if it's not causing you any symptoms or problems and the murmur is not affecting the hearts performance then it is likely an innocent murmur.
An innocent murmur basically means that even though there may be an abnormality within the heart causing the murmur, unless it's effecting the hearts performance, it is quite normal and no action needs to be taken. Most innocent murmurs occur because blood is being pumped faster than normal or usual.
With regards to the antibiotics, your
dentist is out of date basically. Up until a few years ago, when any patient with a heart valve issue had
dental surgery, Antibiotics were given as prophylaxis to prevent bacterial infections which could affect the heart. If you have a minor valve issue (which often cause murmurs), you are in theory, more at risk from
Endocarditis. Dental work poses a risk because it's dealing with the mouth and gums which can lead to bacteria entering the blood stream and attaching itself to the heart valves. This is a very rare risk.
However the British Society for Antimicrobial
Chemotherapy (BSAC) says that Antibiotics are not needed in most situations.
Their information aimed at patients says:
"After a very detailed analysis of all the available evidence they have concluded that there is no evidence that dental treatment procedures increase the risk of these infections."
In light of this evidence NICE changed their guidelines and are now longer recommending that antibiotics are given before dental work (unless you have prosthetic valves etc).
If your murmur is innocent and is not causing you any problems then there is no reason why it should have any effect on your life or health, I don't know what sort of murmur you have exactly but it doesn't necessarily mean that your child will inherit one too.