Well, the lawyer was either misinformed or lied. There is no automatic upgrade and never has neen (with one small exception for folks charged with AWOL
from the Vietnam war)
So, that begs the question, can you upgrade now?
You can, certainly it is possible...but it is not an easy prospect.
The process is straightforward. You can begin the process herehttp://www.archives.gov/veterans/military-service-records/correcting-records.html
There is also a very good overview of the process here
To be successful, you will need to demonstrate, under the circumstances, that an upgrade to the charachterization is the appropriate result in your case. Typically this would be done by showing that the result at the time was wrong for some reason...for example if there was some error in the process that was not addressed at the time, that would be a basis for upgrade.
The board will also consider your post service conduct, but this to a lesser degree than than your service conduct.
You should start with a request of your records. You can request them here
Unlike the urban legend, there is no "automatic upgrade" for discharges...in fact only a small percentage of requests are granted.
To have the greatest chance for success you should consider working with an attorney that can help you assemble the package you will submit. A google search under "military lawyer upgrade discharge" will net you several prospects...I would talk to several to see if one can be of help...but understand this is a long shot...beware of promises.
The one thing the lawyer can help with is organizing the information you have to put it into a "package" that will make it easy for the board to see your points. This can be a very valuable service.
BotXXXXX XXXXXne: Its possible but difficult to do.
Let me know if you have more questions