Walt Thank you for your elaborate response.
If this is all accurate (and I sincerely hope some of it is exaggerated for dramatic effect), this is horrifying to read. I mean, the whole "no masturbation ever" thing seems oppressive enough by itself, but between the limited privacy and nighttime restrictions, the notion that she would expect you to just endure the pain of wearing an unfamiliar cage and the fact that you still consider her supportive after all that, you can consider me quite shocked.
I second Sasha's and Milord's questions about punishment and nighttime restrictions.
Has your mother ever made any indications what it is that has her so categorically against masturbation? I understand being against excessive masturbation if that has caused you trouble in other areas of life before, but being completely against masturbation to the point where you would consider such drastic measures usually has other explanations behind it.
On a related note, how is your father involved? Is he still in the picture, and if so, what are his views on your situation?
Also, I recognize that it would be very difficult for you to negotiate release breaks if your mother's main concern is any form of masturbation. However, that does not mean you would not be able to negotiate more privacy for yourself while still remaining under the cage's control - however, that negotiation only has a chance of succeeding if your mother has something to lose by not agreeing. And if a strain on your relationship is not enough or too much for you to bear, and your mother is confident that you would not give up the financial support for that privacy, it may be difficult to use her desire to prevent you from self-pleasure (and probably also premarital sex) as a bargaining chip. For an example of someone who was successful despite the parents being categorically against masturbation, look at @Lukas and his sister.
As for your social life, do you regret not getting out more? Would you be willing to talk about some of the awkwardness you have experienced that you are trying to avoid?