Is it normal to be so dependent on my girlfriend?

My girlfriend and I have been together for 2 months now. Our relationship progressed very quickly, and we very quickly fell strongly in love with each other. Right from the start, we've seen each other almost every single day, and we've never gotten fed up with each other. Our sex life is also great. Up until a few days ago, the longest we'd been without seeing each other was one full day.

But last Friday, she went to work in the morning and I left her house as she did so, and we'd already discussed that we weren't going to see each other until Monday; three days without seeing each other. This was because she had college work to do and she is moving house soon so she had to pack all of her things away. I also think she felt bad about not spending as much time with her family because we're always together.

I dreaded this break because I know that we both miss each other like crazy even after just an hour without being together, and she has even cried before from missing me after a few hours without me.

I don't have a job or go to college or anything, because I'm still looking for work, so I don't really have much to do. All of my friends are busy with jobs or college, so all I really do these days is spend time with my girlfriend.

So those three days were really hard. I regularly found myself trying to do things just to feel better because me missing my girlfriend actually made me feel sad and almost depressed. I didn't feel like doing any hobbies and even sort of lost my appetite, but I have also been ill for the past few days so I thought that might have been why. We still spoke on Facebook and called each other lots, and that made me feel happy, until we had to end the call.

I think about her every single second that I'm not with her and sometimes get upset from it, but it's never been this bad. It makes me frustrated that I depend on her so much to feel happy and to have fun, and I worry that I'm always going to be like this with her.

She handles this kind of thing way better than I do, too. So she misses me but she doesn't usually feel too sad from it and she still gets on with life and things she usually enjoys, and work/college etc.

We did just go from Christmas eve 'til New Year's Day constantly together though, so maybe I got so used to being with her all the time and having no resposibilities and just being able to chill and do whatever we wanted. I dunno.

But it feels like something has changed in me after these 3 days and I can barely cope with not being with her, so much so that I'm even starting to feel nervous/sad/worried while I'm with her, almost like I'm just waiting for the moment she has to leave and I'm all alone again, which I don't want to do. I want to enjoy and cherish the time we're together and just completely focus on her.

To give you an example of how seriously obsessed I am with her:

I spent all Monday evening and night with her, all Tuesday evening and night and all Wendesday (today) with her. I'm seeing her on Friday from around midday and I will be with her constantly until Sunday evening, but in between those days, she's at work, on Thursday (tomorrow), and I'm already feeling sad because she just left my house to go home and I won't see her until Friday.

I wish I didn't miss her this much but I do. It can't be healthy.

Also, I have spoken to her about this and told her all of this and she comforts me and supports me and tells me I should look for jobs and find things to do, and it sort of helped me feel better for a little bit but then I felt weird/nervous/sad again.

Is this just like honeymoon period or something and it will pass or is it stupidly weird and not a normal thing in a relationship?