I'm 18 and about 2 1/2 weeks ago I had protected sex but my partner was very rough with it. After we were done I was spotting a little and it lasted about 2 or 3 days, then a brownish color appeared! Now I am experiencing cramping a lot but my period has not came on, along with the cramping I have been having back pain and side pain, bad head aches and nausea. I took a pregnancy test but it came out negative! I'm so worried and can't stop crying. Please help me

If he was rough most likely he just damaged you inside a wee bit, it should heal in a week or two max, if you're still experiencing it after a few weeks then take a pregnancy test. If the condom was securely on, no rips, you should be fine, obviously not 100% but I think its unlikely.

I will assume it was rough because you wanted or enjoyed it rough, I will address that first.
If it is harder than you want always tell them to stop. Next if they do not do enough foreplay even regular can be "rough"

Next you said you used "protection" I will assume that means you only used a condom, which I am sure you know has up to a 10 percent failure rate.

So yes of course you could be pregnant, having sex can cause pregnancy, there is no 100 percent safe.

When is your next period due ? Are you late ? You have to wait till a week after your period should have come if you miss it.