Transferring Games

So I went to transfer my physical copies of the Sims 3 and most of it's expansions from my PC that's dying to my new PC. I read a thread that stated that if you talk to an agent that can give you a file called "entitlement" that'll let you transfer everything. The first agent I talked to showed me what to do and walked me through the first 2 games. Then I went on my own to do the rest. However, I ran into a problem with 7 of the expansions so I went back to support. The second agent said there's nothing I could do about it and basically all those games were gone. That once you redeem a code like I did 10 years ago that the game is stuck to that computer. She did help me merge EA accounts because one of my accounts somehow had a few expansions so I didn't lose those expansion packs. However, now the expansions that were on my deleted EA account aren't showing up through my EA account they're only showing up in the launcher. I'm concerned that since those expansions are only in the Sims 3 launcher that I'll lose even more expansion packs when I get a new PC eventually. Did something go wrong with the merge or that's just what happens?