does that mean that blockchain.info now holds my private key?
Yes, but not exclusively. You still have your private key on paper, so you still hold it. If you don’t (i.e. you lost your paper wallet or destroyed it), you can still get your private key from blockchain.info.
In that case, I won’t be able to add my wallet into another similar app because it’s already synced with blockchain.info with my private keys!
No, that is not how Bitcoin works. Anyone who holds the private key can spend your Bitcoin. You also hold it on your paper wallet, so you can still import it into another wallet software. There is nothing that prevents you from doing that; it’s not like something that can only be imported once.
If you don’t want blockchain.info to have your private key, just make a new paper wallet and send your Bitcoin there from blockchain.info. If you want to access your Bitcoin from a different wallet than blockchain.info, then just import your private key into a different wallet.