If you don't have an obvious thing in the crease of your leg like a cut, or a big boil or pimple, the pain might be a pulled muscle. I would not think it would be related to your period beginning early. Pressure in the head could be because of the time of year -- it's cold season with a bit of the last of allergy season added in. (And of course, if you are now indoors most of the time with the windows shut, it's indoor-allergy time of the year. Even our pets who don't make us stuffed up at other times of year can be harder on the allergies in the winter.)
So, do you stretch? I'm wondering if this isn't a muscle issue. It's always on one side? I would tell your mom about it. We moms like to help! :>)) There are a lot of muscles and ligaments in that area, more than you may think and exertion when walking may be creating the pain. (stretching may help as well as regular exercise). We've also got lymph nodes in that area. If you have been sick or fighting off sickness, that can also be uncomfortable in that area. I agree too with anniebrooke that this all could be related to your period starting. And that head pressure otherwise is probably not related to the groin pain.