That cough your kid has could be a Mycoplasma pneumoniae infection. The bacteria is what causes walking pneumonia, and the CDC says infections are on the rise across the board this year, but particularly among kids ages 2 to 4. The New York Times paints that as "striking," considering the bacteria is more typically seen in older kids. Those who are infected don't necessarily end up with pneumonia; in fact, only about 1 in 10 people infected with Mycoplasma pneumoniae actually develop what tends to be a less intense form of pneumonia (hence, "walking pneumonia").
The Times notes cases tend to spike every three to seven years in the US for unclear reasons. The Telegraph reports Japan similarly usually sees a spike every five years, but is currently experiencing the highest number of cases since record-keeping began 25 years ago. The "why" behind the current rise isn't yet clear, though one pulmonary specialist says tests to detect the bacteria have gotten more sophisticated, which could play a role in the count uptick.
Doctors say the symptoms present much like those of COVID or RSV: dry cough, fever, headaches, and fatigue. The main difference is that symptoms, particularly the cough, tend to worsen as the weeks tick on, and can persist as long as a month. NPR reports at-home treatment (hydration, rest, fever-reducing medication) is usually sufficient, but antibiotics can help with worse cases; it notes Amoxicillin doesn't work though; a macrolide antibiotic like Azithromycin is required. (More pneumonia stories.)