I’m gonna attempt. Are you, per likelihood…

A Tamagotchi? Probably Nyorotchi, this one https://tamagotchi.fandom.com/wiki/Nyorotchi

I used to be born within the 90s.

Tamagotchis have been born within the 90s

People love me regardless that I’m filled with sin.

Nyorotchi resembles a snake, which is the encarnation of sin within the holy bible. Nevertheless you continue to maintain him and provides him meals/cleansing

Committing a few crimes much less would not have modified who I’m.

To evolve to Nyorotchi a tamagotchi child must have loads of failures, comitting two or three much less whenever you’re locked into Nyorotchi, doesn’t matter, you will get him in any case.

I can not change even when the punishment is as extreme as chopping off each my arms

Well, that is the half I cant determine, however I assume is so simple as that Nyorotchi doesn’t have arms, really he has a tail.