Maybe. But there is way to little information in the question. All state agencies have different rules related to licensure or certification. And though it seems unlikely that you could get the offense expunged, it may be eligible for an order of non-disclosure, though that will not keep it from all agencies.
I recommend you contact an attorney versed in administrative law and discuss these matters.
This answer is limited to the facts presented in the question as posed above. This answer does not create an attorney client relationship as 1) I do not know your identity, or 2) have I ever spoken with you. If you feel you need legal representation, I recommend that you consult with a licensed attorney in your jurisdiction. I am licensed in Texas
If by "convicted" you might mean you received and completed deferred adjudication probation, then depending on the type of charge, you may be able to seal it. However, the state board will still be able to find it.
You cannot get charges "lowered" after conviction.
The only possibility is post conviction habeas is there is a constitutional issue about your case or a pardon which is almost impossible to get in Texas.
If you successfully completed deferred probation, you can get the record sealed. But a state board could still see that. If you were convicted of the offense, you are stuck with.
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You can only have charges sealed - or file a motion for nondisclosure if they they werer discharged by a deffered adjudication. If you pled to jail or a fine etc. then they are part of your criminal history forever unfortunately.