The SDDR-117 reader is only for Memory Stick (that’s a specific format, not a generic term) cards, not SD cards.
A question: you bought a micro to full-sized SD adapter for “your” USB reader, THEN you bought a reader? Did you already have another reader, then you bought the SDDR-117 (and if so, did that one not work either?), or did you just mean to say you bought the adapter before the USB reader?