Will migraine headaches eventually go away on their own?

They could. Some people's migraines just run their course for the day and they wake up the net morning feeling fine. For others, it's a little more complicated - they may need medications to help stop the migraine. A migraine lasting more than 72 hours is called status migrainosus and these can be helped sometimes with steroids, but that's something to see your doctor for. Good luck!
Maybe. If you are female, and they are hormone related, then yes, once you go thru' menopause, they should diminish. In the meantime, google "cryotron" to find a dr near you to help treat it.