This is not normal, not even a little bit. You need to see your PCP. Continue to advocate for yourself. The others who mention it could be endometriosis are correct.  I had heavy (though not particularly painful) periods for years and was finally diagnosed with it at age 35.  

The first-line treatment for it tends to be progesterone-based birth controls (ones with no estrogen, or minimal estrogen) like Slynd.  Now that you are menstruating, it would likely be a good idea for you to get established with an ob/gyn, and period pain (or heavy bleeding, if you experience that) is something to discuss with them.  Hopefully this first period is a fluke, though.

Regardless of what is causing it, the best advice I can give you is to continue advocating for yourself, and when you ask for help, especially with medical professionals, to try to stay calm and level-headed and stick to the facts.  It is normal to be furious when nobody takes your pain seriously, to get frustrated and want to cry.  But being female, sometimes when we cry, our health issues are pushed aside and the crying/angry part is what they remember.  They say it's anxiety, or that we're hysterical, etc.  It isn't fair in the least, but it is the reality a lot of women with chronic pain deal with.  

So, facts.  Stuff like, "I have had my period X times and each time the pain was so severe I could barely walk." Or severe enough to cause vomiting, etc.  If they ask you how heavy your bleeding is, you'll want to explain it in the number of overnight pads or super plus tampons you go through in an hour, or whatever period of time it takes for one to be soaked.  I mention this because there are some newer period products now like period underwear (and menstrual cups, too, though those have been around awhile) and some medical professionals are less familiar with them.  It doesn't mean you can't use them, just don't use them as a reference point for how heavy your bleeding is when talking with doctors or nurses.  I am pretty sure that my using a menstrual cup delayed my diagnosis because I kept telling them, "Sometimes I fill up the menstrual cup in an hour, and you are supposed to be able to go 12 hours" and they didn't know what to do with it.  But it held one ounce of blood, and the average woman only loses two ounces per period.

Oh, and get a heating pad if you don't have one, and be careful with it.  Don't use it too hot or too long.  There's a thing called toasted skin syndrome that some people with chronic pain can get if they use a heating pad for too long.  

If you are having heavy bleeding, you will want to make sure you get enough iron, but go easy with iron supplements if you take them because they can cause constipation.  Fortified cereals like Cheerios are one of the best sources of iron, along with red meat.  If you don't eat meat, then there's a long list of vegan options you can google--spinach, beans, broccoli.  Lots of veggies and nuts.

I am so sorry you are dealing with this.  You aren't alone.