You can run your AC, but probably nothing else. Your AC will pull between 10-13 amps, depending upon your brand and style. Anything after that has to fit in within the total available 15 amp range. If you exceed the 15 amps, the most that will happen is, you'll pop the breaker at the service pole (plug).
We used a 15 amp service at home comfortably for many, many years. When the A/C was on, we never ran the microwave. When we ran the microwave, we turned off the A/C first. We ran the water heater on propane. The refrigerator uses about 2-3 amps when it runs, and then we had our cell phones and computers plugged in and television. We never blew a breaker.
Last Fall I took the time and expense to install a true 30 amp service just for the camper. Now we can run everything, just like at a campground.