A few things I can tell you:
If you were arrested, the NCIC database will always show that arrest - a pardon or expungement will not result in removal from that database -
If you are or have been convicted and the court or law enforcement agency sent the appropriate records to the FBI then the conviction will appear on your NCIC record
Each state has different laws with respect to sealing, or expunging records - you will either need to look at the statute in your jurisdiction or get a criminal defense attorney who knows what he is doing -
some folks said "get a different judgement" - if you have been sentenced it is too late - if your case is pending, you have all kinds of options - again depending on the state you live in - you might get a conditional discharge, court supervision, a prosecution diversion program, a deferal etc.....
You need to explain what your goal is and where you are in the process - under and ounce is a misdemeanor or petty misdemeanor in most states and if it is a misdemeanor where you recieved the charge you may not need to worry about it much unless you plan or working in law enforcement, joining the military, getting a federal student loan or working in a private sector job that has a problem with a drug charge then it might not be that big of deal to you -
If you are interested I can give you specific suggestions about how to handle this or who you should talk to - my email is firstname.lastname@example.org