@mrtryhard012 As EA_Illium said, Apex Legends does not have cross-progression. You can link your EA account to both platforms, but your skins/Legends/heirlooms etc., are account specific. If you log back in to your account via Origin, all of your skins and whatnot, will still be available to you when you play on that platform. Any items that you purchase on your newly linked Xbox account, will ONLY be available for use when you are playing on Xbox.
I believe cross-progression is still slated for launch this year, but from what I have seen, this will NOT include account merging (having all your skins on across all accounts). There are other recent threads on this forum, with more information about what is coming up, in that regard.