How can I know if a landing exceeds the hard landing threshold for a Cessna 172S?
Was it uncomfortable or did it hurt?

If it hurt you, it probably hurt the plane. That 500 pound engine is hanging a foot and a half from the firewall by four bolts. It's not hard to cause some damage.

Anyway, if you think it needs to be checked, just say something to the mechanic. It's not that time consuming, and it's better to be safe than sorry.