Reddit reviews Portable PM2.5 Detector Monitor Air Quality Detect PM 2.5 Monitor Haze Dust Tester Meter High Accuracy for Indoor Outdoor Car Measurement by IGERESS…

Cheapest I found with some quick googling. What you are looking for is a "PM2.5 sensor" if you want to do some searching

If you are handy with electronics (arduino / raspberrypi etc) there are some PM2.5 sensor boards you can pick up for <$20. You could even hook it up to a PC using a UART adapter, if none of that made sense then ignore this :) I have ordered 4 and plan to make a simple device that lets them report their readings over WiFi so I can install them around the house to see how things change over time

The super cheap option if you are concerned for your kid's health NOW is to get them a face mask, "N95" is the term you want to search for as masks with that rating will filter out the dangerous PM2.5 particles. Amazon has a load and some of the cloth ones even have fun patterns on them and come in a range of colors to make them more appealing to wear, you should get your kid one anyway for the walk too and from school and even in your car as car filters do little to stop PM2.5 particles, you may as well have the windows down if that was all you were concerned about filtering out