I didn't want to post this publicly.
My feelings on sex are very similar to yours. I have also wondered about asexuality myself. Based on my research, I have decided that because there are times (though rare) that I want sex I am not asexual. I see other people that, objectively, I know are good looking, but I really have never felt physical attraction to anyone -- even model/celebrity types. Everything for me is about the emotional connection. I would probably be fine never having sex again. It seems like this is similar to how you feel, too.
I have been in a very happy relationship for almost 3 years. My SO has an extremely high libido. This has caused some issues, but nothing that open communication can't solve. I get a lot of non-sexual pleasure from feeling desired and from pleasuring my SO. This feeling seems similar to how you described yourself in your post. I keep a running count of sexual acts we engage in per week to make sure I don't neglect my SO sexually, and I also monitor the time between acts to make sure it's never "too long."
Basically, I wanted to tell you 3 things:
1) I don't know if you/we are "normal," but who wants that anyway? You certainly aren't abnormal. More important than being normal is being comfortable with who you are. You sound very self-aware, and that's great! Trust yourself and be your own friend.
2) I think your worries are a little premature. don't worry about how a future SO might react to you. When beginning new relationships, I find it best to be sometimes too honest about myself and my feelings on sexuality. If a potential mate takes issue with my perspective on sex, our relationship would never work, and there is no reason to pursue it any further.
3) in a relationship, there is no reason to sit around wondering how your partner feels. If, in the future, you're concerned that your SO can tell that you don't experience physical sexual attraction, it doesn't really need to become an issue. First, your partner should know that about you before you begin a serious sexual relationship. Secondly, you should both be comfortable confronting things that bother either one of you.