I haven't heard of anti-m before but I just googled it and it sounds as though it is similar to anti-d except that complications with anti-m are very very rare.
So basically the concern is that your blood has antibodies that will attack antigen m in your baby's blood IF your baby has antigen m. They might want to test your partners blood to find out if he has antigen m because that will give an indication as to whether your baby might have it.
Now, your anti-m antibodies can only attack your baby's m antigens if your blood mixes with your baby's blood which happens if you have a placental bleed eg like what some people have with placenta previa or if you have trauma of some kind to your bump which causes a bleed. People with anti-d get an immunisation of sorts to protect against this but from what i can find, they don't do it for anti-m because it is really REALLY rare that complications arise from anti-m.
They usually have a titre level that is acceptable for the anti-m antibodies that they can measure. They might want to monitor you later in your pregnancy and check that the titre levels remain the same and aren't going up. Sounds like this might be the tests your doctor was talking about. otherwise it sounds like you haven't got anything to worry about. You should expect everything to continue to go the way it has up until now.

As I said, this is what I've just found through google - don't know much about anti-m so this is just as reliable as google! But everything I could find basically said you shouldn't worry about it.

Maybe someone else will have some more expert advice for you but in the meantime, I would just relax and try not to worry about it. (hugs) it is always scary to hear something you're not expecting.