"A régi cipőm azon a polcon van."

Translation: My old shoes are on that shelf.

[AlsEenPoffertje]

Is there any way to differentiate between "my shoe" and "my shoes" in Hungarian?

[vvsey]

A bal cipőm és a jobb cipőm. Left and right. But if it is the right one, clarify that it is not the "better" one.
You can also say generally: "fél pár cipő". Half a pair of shoes.

[AlsEenPoffertje]

Ah, okay! Köszi! :D