Pinning latlong points on downloaded openstreetmap shapefile

I have downloaded the florida openstreetmap shapefile zip files. I have a dataset with zipcodes and i want to match the zipcodes to points on the shapefile map. I am using sas. I really can't find an example on this. Also i have to mention that I can't connect any information to nominatim or any online search of the zipcodes it has to be from a downloaded map. Is this possible? Or does the open map data shapefile not include zipcodes? Thank you in advance. I feel super lost and have never done any map visualization.