Scalp tenderness that comes on a couple of days after a wash and gets worse with touch or pressure usually points to scalp sensitivity, not something serious. Tight hairstyles, product buildup, or simply tension in the scalp muscles can all cause tender spots like these, especially on one side if you tend to sleep on it.
Next Steps
Check the tender spots for a visible bump, redness, or flaking, since that would need a dermatologist instead. Try a gentler shampoo, loosen any tight hairstyles, and see a general physician if the pain continues past a week or spreads.
Health Tips
Get it looked at sooner if you notice swelling, fever, or hair loss at the tender spots.