Radio waves are fairly high in frequency and are well above the frequency range of your mic input. There are oscilloscope programs that use your sound card’s input but they are restricted to audio frequencies. If you just want to demonstrate AM vs. FM they’ll work, though you’ll have to find audio examples of each.
You can buy external oscilloscopes that hook up to your USB port. The higher the frequency the higher the cost, generally speaking. Note that most oscilloscopes these days are digital, and they advertise the sampling frequency, not the highest frequency that they can handle. A 100 MHz oscilloscope will have a 100 MHz sampling rate, which means it’s not going to be of much use for anything above 10 MHz (well below the FM radio band).
Also note that radio signals are pretty weak, unless you happen to be fairly close to the radio transmitter. Just sticking an antenna on the front of an oscilloscope and hoping for the best probably isn’t going to yield useful results.
My personal recommendation for a cheap scope is the DSO Nano from Seed Studio, which is a tiny little pocket sized scope. It’s less than a hundred bucks and has a good sampling rate. On the negative side, it ships from China (not obvious when you buy it) and its interface is extremely unintuitive. It won’t display on a PC, but you can take screen captures and download them to your PC using USB. I have no affiliation at all with this company other than I bought one and I’m fairly happy with it. It won’t replace a proper high frequency Tektronics scope though.
Here’s a sound card scope. I haven’t used this one, but I believe it is free for non-commercial use. Note that a sound card scope will not be able to handle DC signals and will be limited to about 20Hz to 20 kHz.