I'm currently on birth control I have been for 4 or 5 months I take my pill about the same time every day never missed one. I just started my period today but lately I been feeling my heart beat pretty strong in my stomach for a couple weeks all day and night could I be pregnant still?

Any time you have sex pregnancy is possible. Birth control, even when used correctly, isn't 100%.

So yes, you could be pregnant. That's always a possibility any time you have sex.

Even if I have my period ?

You didn't mention that in your post.

Although unlikely that you're pregnant if you have your period, some women do experience bleeding, which they mistake for a period, throughout their entire pregnancy. Rare, but it does happen.

If you have your period then why are you concerned about being pregnant?

Yes I said I started my period today
If you read back but I'm worried because I've never had this feeling in my stomach of my heart beat all day long and all night too I've had it for weeks

If you're worried then take a pregnancy test. Really, we can sit here all day discussing your symptoms, but none of that will give you an accurate reply. The only way to determine pregnancy is with a pregnancy test.