A doctor cannot force you to stop diving. What they can do, is to recommend you stop diving, but the decision is still yours. At least that's the way it works here...
What they also can do is give you valuable information about weather or not you have some more serious underlying problem or if it is indeed just a blocked or dry sinus. Just for the sake of knowing and reassurance, I would recommend a checkup if such problems persist. And go to a dive doc, who may actually know a thing or two about how sinuses etc work under pressure.
It is not uncommon to have a bit of blood in your snot once or twice in your "career". Most divers encounter that before they learn to equalize and learn to know when it is just better to stay on the surface.
But to have a bloody nose every time or regularily means there is either something wrong with your body or the way you dive - or both.
Let's remind our selves of one very basic thing. Blood is supposed to stay in the body. Blood outside the body means that something is broken. It may be minor, it may be major, but broken none the less. It should be let heal or in some cases fixed via external means (surgery etc). Not letting it heal will only make the problem worse.
From experience I know that if you have injured a sinus, to let it completely heal you must take a total break from diving for several weeks, and after that start gradually building up again.
A friend of mine suggested for me to take Sinus Meds before diving, But I find it makes me dry up quite a bit.