I wouldn't worry too much about it. The only thing that concerns me is that your DH is sort of setting the situation up as a test of her competence! I don't think that's entirely a fair way to see the situation.
I'd just mention it. A simple explanation is sufficient--"I seem to have gotten all these broken blood vessels in my face from coughing too much." If you don't want to discuss it with her. Or if you do or if she asks questions about why you were coughing so much, continue with "because I got really upset and was crying hard." There is not a woman in the world who has not gotten upset and cried while pregnant. Or while not pregnant! Having emotions is nothing to be ashamed of! And you are not required to go into the details of the upsetting event/"tantrum" with her unless it is pertinent to your care or you wish to discuss it. I wouldn't worry about it--trust me, midwifery is one of those professions where you have a real window into human nature, and this is MINOR compared to some of the stuff she sees/hears!!
I have similar things happen to me--actually, if I get really upset about something to the point that I cry really hard, I throw up!!! A few weeks ago this happenned because I was crying only a little but was nauseous already because of something I'd eaten, and then my face had so many little dots I looked like I had some terrible disease! It went away in a couple of days.
: My midwife is doing a home visit tomorrow morning. I'm really embarassed to admit this, but I had a real full-blown 2 year old style tantrum this afternoon. And as a result, I've got those little broken blood vessel pinpoints all over my face and around my eyes. Granted, they are probably due to the coughing fit that ensued from all the crying, but still, I'm a grown woman and shouldn't be throwing fits. Doesn't speak very well to my mental health. 
