Hi there and welcome. First let me set up the disclaimer that this is an internet web site and no one here will have THE answer for you. Only a doctor can diagnose you.
Hormones do affect us in many ways and headaches is a common issue. I myself get headaches related to my hormones. Usually worse right before or during my period. I'm prone to migraines so shifts in the hormonal balance affect me. You may have this same type of sensitivity. Dehydration can also cause headaches. So, mentioning that since you asked about dehydration. The shortness of breath ---- well, I'm doubtful that is related to be honest other than you're generally not feeling well or as you said, dehydration.
Hard to say if you are pregnant as you did have unprotected sex last month. If you don't wish to be pregnant---- I would use protection each and every time religiously. Or get on birth control.
Good luck dear
Some women get migraines with their periods. Migraines don't have to have an aura, and sometimes the aura isn't the classic seeing bright lights or spots or other visual things. Talk to your doctor about the headaches.
I suspect the being out of breath while running is unrelated.
I had a neighbor recommend this to me and it has been really helpful. Drinking gatoraid and a lot of it during a headache episode seems to help me. Not sure the correlation or if there is one but just an fyi for something I do that helps a little. peace