The FGB prefers mo chuid éadaigh. The NEID has a preference for mo chuid éadaí. (éadaigh is the genitive singular, so this is " your clothing", éadaí is the genitive plural, for "your clothes").
You will encounter m'éadaí, though it's considered béarlachas. mo héadaí is never right, because mo and do always contract to m' and d' before a vowel sound, whereas na doesn't, so you would get m'éadaí (if that was correct) but na héadaí.
(Edited to note that the FGB says cuid éadaigh).
It seems that um is used instead of ar in the sense of putting clothes "on"; when it's reflexive, Duo seems to accept "(put) on" as a translation. So the sense here is "she's putting my clothes on me" (like a mother dressing a child). But I'm just going through the lesson myself, so I might be wrong. :)