I made my older brother cry?

I am 14 and my brother is 17. We've never gotten along and always bickered, but I thought that's what all siblings do. Lately, we have been fighting a lot more, and he has even cried on a few occasions because he says no one in our house ever gets a long and we fight all the time. We never get into physical fights, just arguments. Well for the past few days, my brother has been telling me to just pick up some stuff around the house, but it is regents week, I am entering a freestyle with my dog next week, AND tech week of the show that I am in, so I am very busy from rehearsal, studying, and practicing freestyle and didn't get around to putting my stuff away. Well today, my brother told me to put my stuff away, he said "Put it away NOW. I have told you to do this for days" I said I would do it in a bit, but I had to finish practicing with my dog and studying, so he told me about 5 more times within the next hour and a half and I kept telling him that I would do it when I was done, and then he freaked out and was like "NO! YOU HAVE TO DO IT NOW!!! I HAVE BEEN TELLING YOU TO DO THIS ALL NIGHT!!!" I said "okay" and went upstairs and emptied the waste basket and picked up my other stuff (but I did at a rude remark about him being so nagging) and then went back to my studying. Well apparently I didn't put something in the waste-basket, and he freaked out AGAIN, I said "OMG why are you freaking out so much!? Anger management problems! Jeez!" he said something along the lines of "YOU PIECE OF S***! YOU CAN'T DO ANYTHING RIGHT! YOU ARE THE REASON WHY EVERYONE IN THIS FAMILY FIGHTS ALL OF THE TIME! YOU ARE THE REASON WHY DAD IS SO STRESSED! YOU ARE SUCH A B****! IF MOMMY WAS ALIVE SHE WOULD BE SO DISAPPOINTED IN YOU! YOU NEVER CHANGE! I HATE YOU!" and continued to scream at me from his bedroom for about 3 more minutes after bursting into tears. I didn't feel like I did anything that terrible, but I feel really bad because my brother rarely cries, but has been doing it a lot more lately, and what he said was really hurtful. What should I do? I don't want my brother to hate me forever, but I also don't think I should have to give him an apology because I really don't think I did much wrong. Yeah, I didn't do my chores when he asked me to, but I DID them! What should I do?