Hi, I've been seeing (and fucking) this girl for about a month and a half now but only recently (like a week or so) we agreed to be exclusive. I know that's very fast, and probably mistake number one. But honestly, she is my first girlfriend and I figured I'd do it also to get some sexual experience under my belt.

We live an hour and a half apart because in this month and a half I started university. I only see her on weekends. When we do, we have sex. Now, yesterday she texts me what I'm up to, blah blah, standard conversation. I aks her "what are you up to tonight?" and she says "I'm seeing a friend [male] because he wants to celebrate he's found work".

No problem for me, but there's a couple of catches that make this case special:
1. It's 10 o'clock in the evening, on a week day. When I have girls over that late, it's surely not to be FRIENDly with her.
2. I know this girl from our social circle, and some of her friends casually mentioned that that day (the day she went to her friend) would be the 3 year anniversary with her previous boyfriend, whom she only broke up with two months ago. (Should've been a red flag for me I guess since she fucked me only two weeks after she broke up... but whatever) and they have also casually mentioned (without knowing better of course) he has found a new job recently.
So she is meeting a 'friend', who just found a new job, on the would-be anniversary with her ex, who just found a new job. See what I'm getting at?

I let my emotions get the best of me (big mistake) and I asked her if it's "who I think it is" she's visiting. I told her I thought she was visiting her ex and she assured me it wasn't him but admittedly it was a big coincidence (too coincidental for me). I told her I couldn't and didn't want to stop her from going, but that she has to be honest about me with it. She kept saying it's not him and even told me she loves me (first time the magic words are spoken during the relationship (over FB chat no less)). This has quite the opposite effect she probably intended on me because saying "I love you" during a conversation like this just screams "emotional manipulation". I ignored it and told her to have fun tonight. She said "is that all you have to say?", waiting for a response to the "I love you" of course, but I ignored that too and then she said "do you still want to see me this Friday?" and I said (stupidly?) yes. I told her to have fun tonight, again, and she told me "no I don't feel like going anymore, I'll watch some tv tonight" and then I left to have drinks with my friends. That's the last I've heard of her.

Thanks for reading if you've come this far. My question is, what the hell do I do now? The whole situation is so damn coincidental and I have such a strong feeling she's lying, but I will never know for sure, and she probably knows this too... . Obviously I've made some mistakes too, and I'm very much looking forward to your advice on what to do next.

Yes it does seem dodgy but it also be nothing - exactly as she said. Firstly think about what you know about her - have you seen/observed any dodgy behaviour relating to cheating? If the answer is yes, then she probably is lying and is going to cheat. If the answer is no, then it's probably something innocent.
Did you ask her if anyone else was going to meet up with this friend also? If it was a group of people then I doubt you have anything to worry about. If it was just the two of them, and she was going to his house for drinks, then that seems suspicious.
From here I would have a face to face chat to her and set up boundaries/ground rules for the relationship. Tell her that she does anything physical with another guy then you will dump her ass because you respect yourself too much to allow bad behaviour in the relationship. Also you want to be trying make her feel deep emotions through experiences with you, so that she will get emotionally attached to you and will be less likely to cheat.