I'm 17, I had sex for the first time on April 19, which was one day after my period had ended. With it being my first time I did bleed, but for the next few days I continued spotting a little. I've also been having cramps and light headaches.
Its now April 25, could I be having pregnancy symptoms? Or am I just over thinking it?

Sure it's possible you could be pregnant. Maybe you're not. There is no way for us to know.

You need to see if you get your next period... if not, wait a few weeks and then test.

But to answer the question you asked... Yes, you COULD be pregnant.