Yes! You have misophonia. It sucks, I know. I too have misophonia, and I'm 15 years old. I know what you're going through!
Sit your family down and talk to them about this. And I mean, call a family meeting, make sure everyone is there, and ready to stay there for a talk. Do NOT let them joke around, and explain that this is real, and it is truly affecting you! Show them sites on misophonia, prove it is definitely real. They may not take you seriously, but they will eventually have to.
Go to a counselor or psychologist of some sort. Hopefully, if you tell your parents "I NEED help!", they will take you seriously. CBT (Cognitive Behavioral Therapy, look it up) can help (it's helping me, I'm your age (15 years old) and I'm going to a counselor and she's really helping). Your family needs to make changes, to avoid setting off your misophonia. Hopefully, they will learn that misophonia is real and a very serious problem.
Sadly, misophonia is poorly understood, and it is not curable. I am going to a counselor, and she is helping me deal with the misophonia with CBT and with various other techniques. Seeing an expert is recommended. Seeing a family doctor is also a good enough idea, if you want medications.
Check out these sites for more information and for support:
http://www.psychologytoday.com/blog/brain-babble/201305/misophonia-enraged-everyday-sounds
http://misophoniasupport.tumblr.com/
http://www.misophonia-uk.org/the-misophonia-activation-scale.html
http://misophonia.com/
http://www.misophonia-uk.org/
http://en.wikipedia.org/wiki/Misophonia
And, of course, if you Google "Selective Sound Sensitivity" or "Misophonia", a lot of good stuff comes up.
I know that misophonia is very hard to live with. I've had it since I was around 8 (it started with me hating whistling), and I still have it today. I am 15, turning 16 this October. Misophonia makes daily life hard, but if your family takes you seriously (because you explain it to them, and don't let them screw with you), they can make your life easier. My family and I have learned to cope. They try their hardest to not make any trigger noises near me. And I have learned to stand my ground and ask them (nicely) to stop doing whatever they are doing. I feel bad about asking them to stop some stuff, like tapping (my dad is very musical, so he taps all the time, and it sets me off, so I ask him to stop tapping a LOT) and breathing really loud (I mean, people have to breath... I'd just appreciate quieter breathing, lol)... But that's life now.
So, best of luck! Misophonia is real, and it is a very bad problem. Don't let anyone tell you otherwise. Many people don't believe it, but you and I know that it exists.
If you ever wanna talk, my Twitter handle is @Vimm3l. If you don't use Twitter, that's cool. I don't use Twitter much either! But if you wanna shoot me a tweet, we can exchange emails and talk some more. If you don't have a Twitter, just make one and Tweet me. Or post your email address. I would post mine, but I already get enough spam, I don't want any more! I'm /BAMFchick (don't judge, I made that username in 7th grade, lol) on FACEBOOK, so add me if you want. I'm assuming your name is actually Emily, so add me if you want. I'll accept your friend request and we can chat.
I completely understand what's going on with you, so maybe I can help a bit. I am a girl your age, so don't worry. IF you don't wanna talk though, I totally understand. I'm not some social butterfly, I'm not very talkative, but I am wanting to help someone newly discovering a very important problem like misophonia.