Dude the NCR people that are shooting at you are probably gaurds.. I don't think any one read the faction armor section when it pops up for the first time. Faction armor blends you into that faction EXCEPT for guards... So the guards are usually indicated as a red mark on your little tracker thingy for people. So I'd just try and do a stealth kill of the guards then you might be ok? Or yea you could go back to GoodSprings and do it up there as well.
oh, guard dogs can sniff you out too.
so yea... avoid them... like the plague.
oh, and if you have access to the folowers of the apocalypse, they sometimes have rad away too.
and if that doesnt work, try that doctor person for some rad away.
if that doesnt work... well then you on those types of days where rad away is devoid from the area.