The nosebleed issues are tricky.
The simply and most common explanation is that they result from the enhancement of activity at mucous membranes that occurs during pregnancy. I had nosebleeds out of the blue all through the second and third trimesters of my first two pregnancies. Only in the second did I have preeclampsia.
However, once you stray into the territory of preeclampsia you do need to bear an alternative explanation in mind. One of the extreme varients of preeclampsia, called HELLP syndrome, involves the destruction of blood platelets and that can stop blood clotting well. If they go very low there is a risk that bad things can happen. If you did have a nose bleed, or had bleeding from gums or some other site that was very slow to stop, I wouldn't hesitate to get in touch with your OB or even to go to L&D to get checked.
I know that sounds like a hugely scary explanation and I really don't want you to freak out and worry like crazy. The top explanation is the one that is by far and away the most likely. The best way to deal is to know the warning signs and symptoms, etc. The "headache", visual disturbances, severe epigastric pain etc. are all really good reasons to call and check with the folk overseeing your medical care.
Mom to Finn, Lucy (preeclampsia and HELLP) and Chloe.
Moderator HELLP Syndrome Survivors