Am I being dumb? Paranoid?

[Evina..]

Hello.
So every time I'm curious about something people here always seem to know the answer. And because I'm kind of loosing it right now, I could use some answers.

So I have this boyfriend, and I love him with all my heart. But there are things that don't seem right, and since he's my first real relationship I don't know if I'm just overreacting or if there's something wrong with him.

Example nr. 1: I found some texts of a girl calling him my love, and he called her baby sweety and so on. I freaked out. He swore that there was nothing going on and never was, and that she just talked that way to everybody. After a while I believed him and closed the subject.

Example nr. 2: When I want to talk to him, and he's busy, and I get angry about it, he just freaks out. Now, it's not like I'm sticking to him like glue, we don't even see each other that often.
A few days ago his words were: We've just talked on the phone for an half hour, you are so grasping, you just want attention 24/7. 1 hour is too much?

Example nr. 3: The last 3 days his phone was shut off and I couldn't reach him in any way. He said he was going to his friends. So I opened his twitter, just to see if he had tweeted. And when I saw that same text-girl I freaked out and cried about I just had this strong feeling I had to see her profile. And she had tweets that he was the last 3 days with her, that they had so much fun and that she loved him so much and so on. The tweets continued until 4 in the morning, he wouldn't even pay attention to me because I choked him after being on the phone for 1 hour, but he sat with her until 4 n the morning??
This is what really, really hurt me. I can't explain the feeling, I'm crushed.
So I contacted his sister yeah, bad move I know. But I was desperate for answers and I couldn't reach him in any way. So finally he called and said his battery was empty and he swore he wasn't alone with her and that he would never ever cheat on me.

I believe him, am I being dumb?
And I can't stop thinking about, does he really rather spent time with that girl or am I just being paranoid?
It really hurts so much, I am very patient and I try not to make a big deal, he gets angry when I try to explain that some things he does hurt me, but I am running out of patience.

I am so full, I've got this feeling that I'm about to explode, these are just examples, there are so many things. He just won't listen to me. Please don't say leave him. He is the first thing I think about when I wake up, and the last when I go to sleep. I want to fix it. He of all people is the first person that gave me the feeling I was alive, that I'm a person, and beautiful. He has really good sides.

How can I make him listen to me? Am I making a big deal out of nothing?

I'm sorry for the huge story. And if I made any spelling mistakes, I'm from the Netherlands so please forgive me.

Thank you in advance, for reading and helping.
Thank you for your answers, your advice really helped.
We are dating 8 months by the way