Your post is unclear. If you were "convicted," the warrants relating to the charges upon which you were convicted no longer exist. An active warrant may prevent you from obtaining a passport.
In no way am I offering you legal advice, and in no way has my comment created an attorney-client relationship. You are not to rely upon my note above in any way, but insted need to sit down with counsel and share all relevant facts before receiving fully-informed legal advice. If you want to be completely sure of your rights, you must sit down with an experienced criminal defense attorney to be fully aware of your rights.
Clear up the warrants by doing whatever it was you were supposed to do and surrendering yourself to the court. This is best done with an attorney pre-wiring your appearance to minimize any arrest/booking time.
Once the warrants are cleared, get the passport and have a good time.
Another consideration is that even were you to get your passport, you have the potential that when you seek to reenter the US, the warrant can turn up when you're checked reentering, and you could be taken into custody. I would certainly contact an attorney and get the warrants resolved.