Is it normal to crave intimacy?

I loved my ex in a genuine way. She was a difficult girl to have something with as we both lived in different countries, which made us try having a long distance relationship for a long time. We broke up twice because of the distance, at least that's what we thought was the problem. We thought this because we could never spend that much time together due to conflicting schedules due to studies and all of that. Eventually I decided to do my exchange period in her country in order to be closer to her and "solve" the distance problem. We had fun in her city for three days, after which we never met again during the next five months. She had serious personal issues which made her avoid me in order to avoid potential conflict as she thought she was never ready to meet me during that time. What's left is a very personal and precious relationship that we still share and she told me she wants to try moving to me in about a year when she's done with her studies. After all of that I'm left empty and unfulfilled though, I loved someone more than I thought I was ever capable of doing and right now I just need to satisfy those feelings. A lot of drama happened between us which broke my heart twice, with the second time literally changing me as those broken pieces don't fit in quite the same way anymore. Due to her personal life and past being so complex, we were never able to do anything physical and now all I can think about when I see couples or people being intimate I think of how that must feel like. Both of us, and some other girls that are interested in me but live really far away, have chosen to stay virgins until we find real love (not married). I don't think I can wait any longer. I'm 22, which is young, but I feel like I'm ahead of the curve in maturing emotionally. The problem is that of all aspects in which I've matured, intimacy is the only part in which I haven't grown up at all. I've never experienced it and I feel like it's dragging me down, I also feel a craving for it because of the aforementioned unfulfilled hopes. I feel confused and not sure of how I want to carry on, I've always held the idea of love as the highest importance on this matter and now after changing I can't seem to wait much longer. I never felt this way before all of this, it's like it's the last straw. Is it normal to feel like this? I feel like it's shameful and indecent to think this way.

I began smoking weed in order to "compensate" for these feelings but I don't know for how long that will hold. I had a panic attack due to weed when I lived in her country but even after that I still do it. I need to experience something new I guess.