First, it took almost 60 days to get mine last renewal and that was well before the recent run on firearms and ammunition...so expect them to be slow. Second, some crimes which lead to misdemeanor convictions are often automatically charged as felonies, so its possible something like that occurred. If you were really only convicted of a misdemeanor, you have nothing to worry about.
If I were you though, I'd just bide my time, since they are so backlogged.
However, if its convenient, you could go to the court were convicted and get the pertinent records and mail them to the state police. That might speed things up.
"No free man shall ever be debarred the use of arms."- Thomas Jefferson