Are over-the-counter products effective in treating nail fungus? How will I know when it's time to see a podiatrist? Is prolonged infection dangerous?

No. It may not even be fungus at your age but nail dystrophy secondary to repetitive micro trauma. OTC products aren't that effective but will do no harm if you try.
Possibly. Some of them mav be helpful with minimal involvement. You should consult a podiatrist for proper treatment and follow up. You also need to treat your shoes skin and shower to prevent re infection .