You can reach EA support through the
Customer Support link that is at the bottom of each page on this forum (on full sized browser windows). But honestly, for something technical like this rather than a user account issue, you will be much more likely to get a positive experience by posting on the
TS3 Answers.HQ tech board. There are helpers there who are well-versed in these Steam vs. Origin issues, whereas otherwise you might caught in a "It's not our problem, call the other guys" loop between EA and Steam.
It sounds to me though that you do have elements of an Origin and a Steam install in place at the same time, at least in the Windows Registry if not more readily apparent. I would suggest uninstalling TS3 entirely, both versions as they are not mutually compatible, clean the Registry by way of Piriform's CCleaner (the free version is fine) or your favorite Registry cleaner if you aren't already doing that, and start fresh with no install, no game folder, and proceed on one platform or the other exclusively.