A/C is fully charged, it blows hot and musty air after ten minutes

Hey gang, I have the vehicle listed above Sport model. A/C has run like a dream to this point. Right before summer, I started noticing that after driving for 10-15 minutes, the A/C would just gradually start blowing this warm air that smells like an old hotel room. Once in a while if I shut the A/C off and wait 10 or 15 minutes it will blow cold again and repeat the process. I tried to charge the system, but it is fully charged. Can't find any leaks, air filter is clean. I'm thinking about renting a set of gauges, but I'm not really versed on what and how to track anything down with them. Really hoping it's not the compressor or anything pricey. But I do live in Florida and its smoking hot here. Any help is much appreciated. If I missed any info I apologize in advance. Thanks again pros!