Probably just don't want the other to find out about her relationship with dick, and he plays along for reasons. Likely something to do with amazon girl, starfire or both. Gotta hide that Dick lust.
I don't think that halo will heal her since she's, well, hiding. Halo will not know that she needs healing or that she even exits at this point, most likely future season arc.
That and they haven't yet stated clear reason for her condition, WE know that it most likely had something to do with joker or just general accident of somekind, but in universe they havent yet drawn attention to it in narrative sense, so it's most likely saved as plotpoint for future seasons.