It sounds like this is going to be on your record permanently. That's what a guilty plea does: it turns a charge into a permanent criminal conviction. This isn't going to just "come off on its own." Many states offer a program called judicial diversion, which allows qualified first-time offenders to have the charge dismissed and expunged from thier record following successful completion of probation. However, I think you're too late for that. Diversion generally has to be set up on the front end, before pleading guilty.
On the bright side, this sounds like a misdemeanor and not a felony. Misdemeanors are generally not as bad. They don't carry the same stigma a felony would to employers, banks, schools, and apartment managers. Bottom line, I don't think this can be removed now but if it's a misdemeanor it shouldn't hold you back too much in life. I don't know how it would appear on your record. It would probably at least say Possession Drug Paraphernalia.