Yes. In the last trimester some women get more headaches. I do. And I haven't had a nose bleed in about a month but I was getting them frequently in my 2nd trimester. My doctor said your nose tends to dry up or something which causes nosebleeds. I honestly don't remember exactly what she said but she did say it was normal
If you are really concerned or gets worse, I would call your doctor just to be safe :)
I have heard of this happening and read that it's normal during pregnancy, partially due to increased blood flow