how to change projected coordinate system but keep location

[RachaelNorton1]

I GPS'd some treatment areas and for some reason, they are recorded as Lambert Conformal Conic.  This is not how my GPS is set up so I'm not sure why this has happened.  When I use the define projection tool and set them to Nad 83 UTM 10N, they end up elsewhere, but I need them in their current location, as Nad 83.  Any help besides re-GPS'ing?!?! Wasting days here.  Any help is appreciated!

[RachaelNorton1]

I did it!! So in the layers list, right click and go to data, create feature class.  This opens the create feature class tool, go to the environmental parameters and set the desired spatial reference there. whew!!