Yes. Because both the state and federal governments are separate sovereigns, you may be charged by each, as well as ultimately convicted and sentenced by both. This has nothing to do with “double jeopardy”.
However, this situation is unlikely. Usually, the federal government prosecutes cases of high-volume drug sales, whereas the state handles the local level. Also, federal charges typically carry harsher sentences, and if they are prosecuting a case, other prosecutors may feel that the crime is being properly handled.