I don’t think your desire to have sex with your girlfriend is abnormal. You have a high libido. As I’ve mentioned many times in this column most couples have mismatched sexual desires. Usually one person in the relationship has a higher sex drive than the other.
Because you have a higher sex drive than she does, you want sex more often. You temporarily found a way by “rubbing on her” to satisfy that drive. As far as I can tell you did it when she let you and stopped when she asked you to. Again, I don’t think this is particularly abnormal nor is your fetish for her “backside.” It’s a common fetish.
What may be problematic is that you find masturbation undesirable. I understand that sex is preferable with another person but you have a partner that does not want it as often as you do, and it’s causing major problems in the relationship. If you were to masturbate, then your desire to “rub against her,” something she currently does not find acceptable, would be decreased.
Masturbation can be a difficult and even controversial issue. People tend to have strong feelings about it. For some, masturbation is prohibited due to a religious belief. The Catholic Church, for instance, believes that it’s sinful to masturbate. Then there are some who refuse to masturbate because they don’t think they should have to. Masturbation is “beneath” them, something only single people engage in or “losers” who can’t find a willing participant. I speculate that the latter explanation is much more aligned with your thinking. Perhaps you are of the opinion that because you are in a relationship you should not have to masturbate. You may also believe that if you did then there is something seriously wrong with the relationship.
The truth is that masturbation is perfectly normal and healthy, no matter your relationship status, and in this situation, it could be the solution to your problem. I think you should strongly reconsider your thinking.
If you’re not willing to consider masturbation as a way to satisfy your high sex drive then the two of you need to create an alternative plan that is satisfactory to both partners. This would involve finding an activity that you both could participate in, perhaps something other than straight intercourse. You could explore other options such as oral stimulation or sex toys. If you’re not sure how to achieve this then you could read about it or meet with a sex therapist. A sex therapist is trained to deal with these issues. He or she could guide you on the best way to approach this problem. A few meetings with a sex therapist, in which you both attended the sessions, could be very helpful for the relationship.
I hope this answers your questions. Good luck.