I think my boyfriend is cheating

Your bf is using an app that is designed for one night stands and has a secondary use as a dating app.
Do you really need to post on TSR before deciding what to do?

I have no idea what to do. I know most people will say I don't trust him and that I don't deserve him because I'm speculating of such, but what if I am right?

Your boyfriend doesn't sound like he's being very fair to you or treating you very well. Obviously, it's your right to choose to be with him but I'd question whether I would want to be with anyone who is willing to end things because they 'want a girlfriend they see often'. He's entitled to want that but to be with you and then tell you he'd end things if you got a job with hours that don't suit him makes it sound like he's more interested in a girfiend as a commodity than a person.
If you have concerns, explain to him why his behaviour is upsetting for you. Ask him why he wants to use something like Tinder in front of you. It's obviously intended to make you jealous, and clearly works, but why does he want to make you feel jealous and insecure? That's cruel and manipulative. And if he 'goes off on one' because you point out that his behaviour hurts you then that shows an even greater lack of respect, caring or empathy and really doesn't make him sound like a great partner.
I'd advise you to talk to him, calmly, with no aggresion and try to get him to see why it's hard for you to feel secure when he's rating other girls in front of you. If he can't agree to treat you with more respect then I'd end things but only you can decide what's right for you.

I know my boyfriend has Tinder, he winds me up over it whenever I'm with him, going on it and "liking" all the girls saying "she's hot" and "ohhhh".

We're in a long distance relationship and he's said before in a heated conversation, that if things between us in a couple months doesn't work out because of him working weekdays and I'll probably end up getting a job at the weekend, then he'll end it. He wants a girlfriend that he can see often.

He's never on Facebook Message for any length of time, sort of stares at it and then closes the app down, same with Tinder - and he's got quite a fair few messages on it from what I could see at the corner of my eye. He also pulls himself away/turns around so I can't see anything and it gives me a weird panic feeling in my stomach.

I noticed his most recent Facebook message with a name - of which has been stuck in my mind ever since. Whether or not it was a girl, or I mistook it for someone else, I feel like he might be hiding something from me and I can't confess it to him because he goes off on one at me.

I have no idea what to do. I know most people will say I don't trust him and that I don't deserve him because I'm speculating of such, but what if I am right?

I tried bringing her name up in a conversation, pretending that the alleged girl told me she knows him, but I couldn't keep it up for much longer because he asked to see her profile and where she told me of the sort - almost defensively and in a state of panic...