After doing meditation for some time, how do you experience relationships?I mean..how have your relationship changed?Because..i think I start to care less..
I know many people who really study buddhism and enlightenment, for example monks and people who chose to go with them, do not have relationships.
Is the aiming for enlightenment compatible with having a relationship with a girl?

Are you using the word 'relationships' as shorthand for romantic/sexual relationships? EDIT: or do you mean relationships in general with other humans?
EDIT 2: Either way I'd say it depends on the individual whether meditation will change relationships or not and how but no particular outcome is necessary.

Personally my relationships of all kinds have become more fullfilling and positive the more balanced I become in waking up and growing up. I don't see these two as mutually exclusive but rather synergistic (i.e., growing up opens further possibilities for waking up, and vice versa). One simple change is the less defensive i am and the easier it is to relativize my own perspective-- see it as a perspective- the easier it is to be flexible with others and be open to their differing points of view and take those into account. This makes relationships more fun and fulfilling as well as more  challenging.

Caring less is something that happens for many people cyclically on the path and it can be a symptom of many different things, good and bad. The best advice for a beginner is:

DON'T TAKE YOUR CURRENT MINDSTATES TOO SERIOUSLY!!!!!
Keep an open mind and expect things to change and keep on changing. Be especially wary of feeling that you have it all figured out finally. Also be wary of taking literally thoughts that say everything is falling apart and worthless etc. Learn to take all your feelings and thoughts with a 'grain of salt' (skepticism about their absolute truth); that's a key part of the path and fruit itself!!

romantic/sexual

what do you mean by "Be especially wary of feeling that you have it all figured out finally"?

I recently got into a romantic relationship and then just ended it very quickly 3 days ago. I don't know how to explain my choice to end it and respect her privacy, but I will say how I am changed is nothing really stuck with me.

She got very angry when I told her there were certain things I wouldn't do sexually as they were risky in terms of sexual health. (The reason I ended it quickly, among other reasons)

I just simply felt peaceful and non-reactive from the moment I met her to the moment I dumped her. Like, she would yell at me and before my heart would race but instead I just felt calm, bodily pleasure. I would speak softly and calmly the whole way through her yelling at me, attempting to compromise with her or explain my view. Years ago I would have been desperate to make things work but now I was willing to walk away at any second since I'm just happy in or out of a relationship. 

The best way I can explain it in English is to say awakening is to know God and that knowing God is a much higher priority than romantic love. Because of this, it's easier to focus on Dharma things than romantic love. But at the same time, I feel because I have meditated so much I am a very understanding and fun partner, so knowing God and romantic love actually go together.

First off I'm not suggesting that you are feeling any particular way. Your post was pretty succinct and abstract. My response was general advice that could apply to anyone pretty much anywhere along the path that I've ever met.

The general thrust of what I meant can be summed up by something like "be skeptical of any conclusions you come to about how it is, how you are, etc". Because things change. Things change a lot when you really get into meditation and some of the changes can be dramatic. For instance, for much of your life since puberty, let's say you have been very interested in having romantic/sexual relationships. Let's imagine this has been maybe the major theme of your life. Then you start meditating. Meditation seems to 'work' **-- and something seems to change. Suddenly you find yourself feeling like romantic/sexual relationships aren't actually important, or as important, or whatever; it's a dramatic change.

I'm just saying don't conclude from that "this is how it is! I no longer am interested in sexual relationships!" because a lot of things may be happening below the surface to give rise to that experience. you don't know. It may change tomorrow or next year when you experience another profound 'shift' from meditation. Keep an open mind. That's all

** 'worked'-- according to your preconceived notion of what 'meditation' is ;)

Before (on finding my husband's socks on the floor): What is wrong with him? You'd think a grown man would figure out how to put his own socks in the laundry basket!

After: Aw, my little sweetie, there are his socks! 

and so on. So I don't care, but not in the sense of not caring about him, but in the sense of not caring about what used to be irritants.