Some places have Family Restrooms/Single Person Restrooms which you can use if you are not comfortable using the Ladies Room. Convenience Stores such as 7-11, Gas Stations, and small businesses tend to have single-person facilities. I have found family restrooms at some Targets and at least here in Florida - Turnpike Plazas, but not rest areas on I-95 for some reason.
There is no law that I'm aware of that says you cannot use the Ladies room. Our legislature thankfully killed a bill earlier this year that would have made it a crime to use the correct restroom. Also, some states, counties, or even cities have protections. While, Florida doesn't, the county I work in has LGBT protections.