Hi there!
All ingrown toe nails may not present with tenderness and/ or pus, thought it would be better to confirm a diagnosis with a doctor before initiating treatment. Other possibilities include infections, inflammations, growths/ masses, injuries, neural/ vascular related issues etc. Without an evaluation it would be difficult to point out a single cause. It would be best to get this evaluated by a primary care physician for an accurate diagnosis and appropriate management.
Hope this helps
Take care!