Can i ask my obgyn for refills on my birth control pill if i just ran out of my pills?

You can ask anyone for anything. Whether or not this would fit with the normal routine of a given doc depends on the situation. Often, refills are often authorized until it is time for your regular follow-up exam and testing. If you do not schedule a follow-up within their practice protocol, you are often considered to have left the practice.

This depends on where you have been getting your prescriptions. If you have a regular Ob/gyn doctor whom you have seen recently, they may be able to do this for you. If you haven't seen them, they may not be willing/able to do this. Best to call their office to find out or contact the practitioner who gave you the original prescription if you have seen them recently.