Am i wrong for getting jealous?

My girlfriend has a new friend this semester at university, she showed me a picture that her other friends took of them and they draw a heart, they joke that they are going out.

We have troubles because we don't talk as much like before, I try all day to make conversation but she answer whenever she feel like it and a lot of times doesn't answer all the things that I ask her to make a conversation. We talked about it and she says she is trying but has a lot of thing to do in her life right now.
To be honest, she is really busy and I was with her for a couple of days when she was very very sick.

She showed me a screenshot and ask me if the person she was writing with was flirting, to me it looked that way, but she says no. The name was scratch out and didn't want to tell me who is the person until later, it was her new friend.

Yesterday she came to my house and this some work while I finished mine. All the time she was writing to her friend, and did her work in between.
We both finish working and spent time, she only wants to be in bed with me and show a lot of affection.

I try to have a conversation about that, she noticed that I get upsed because of the writing, ask her why she doesn't write to my like that anymore, we have a discussion and she assured me she loves me and that if she starts to feel something for some else she is going to tell me, that I have to trust her. We end in good terms.

All night she keep looking at her phone and as she was leaving to her house she keeps writing with her friend non stop, I try to look at the conversation and she gets upset, tells me she is used to her privacy I deescalate the situation, she keeps talking to him non stop ask me if we are good and to trust her.

When she arrives at 12am to her home I try to write her, she is online non stop until 2am, in that time, like always, she answer every ten minutes, tells me that she is talking to a girl friend or that she leaves the cell phone on while she put on her pijamas, that I was been jealous. I explained that I was going to stop writing to her so much because she feels like I try to much, and that she loves me, and tells me that she really likes talking to her friend and he make her laugh, that I make her feel like she is doing something wrong, that makes me feel really bad, and we start a discussion again.

Tells me that she is going to sleep at 1am but is still online.
I explained that we started or love with conversations and that is really important to me to speak to the one I love for at least five minutes of fluid conversation that she always had an excuse for that, but I saw her talking to him so much like we used to.

She tells me that she is going to think about that, and to give her space, she didn't want to talk to me anymore because she is tired of the subject