Really need help with my relationship...I feel kinda trapped

This is long, but I really need help with my 17 year old boyfriend. I'm 19. I love my boyfriend so much, we've been together for 3 years. But lately, he's been accusing me of cheating on him...which I don't understand why....because I have been nothing but faithful to him in this whole relationship. Everytime I go out, whether its just to the store, or I'm out with my family, he gets really wierd with me and asks "Should I trust you? Are you cheating?" and then he will be really mad. Its winter break, and this whole break I've been sitting at home, really bored, because I'm afraid to go to my friends house or even treat myself and go shopping because I'm scared he will start getting iffy with me when I'm out in public. Whenever he accuses me of cheating, I get really sad and even start crying sometimes, because it hurts that he thinks this of me. So I don't want to do that in public. I've tried everything.....we snapchat every single day, so he sees what I am up to at all times, and when I have to go somewhere, I always invite him once he starts getting suspicious. But he always refuses to come along. He goes to his friends house every day almost. I never question him,sometimes when we snapchat, he is at his friends house he sends me a black screen....I know if I ever did that, he would freak out at me and tell him to show him what I am doing. I don't question him because if I do, he will get mad at me. It sucks because now since, I sit at home, I get really bored. And when I ask to hang out with him, he gets angry and says I am clingy. But really, I have nothing to do because he will get mad at me unless I'n with him. Like today, I asked him if we can hang out, and he kind of led me on by saying "Maybe...I guess we could" and then he told me his other friend wants to hang out with him so he is gonna hang with him instead...So I don't understand....Im really not happy, at first it was alright, but now sitting at home everyday and having to basically get his permission to go out and even to go shopping and stuff is getting old. I want to get out of the house, but I don't want him to freak out at me. Why does he have to be like this? I let him do literally everything, because once I tried to hold him back like he is to me, and then I grew up and realized that its a horrible thing to do. And all I want for him is to be happy. I feel like he doesn't take into consideration, that sitting at home all day and being accused of cheating really hurts me and scares me. And if he does, he doesn't care. I feel like he is taking me for granted. I know he isn't cheating on me, by the way. We have access to eachothers facebooks and snapchats and phones whenever we want to.