I've multiple wallets and I was wondering if I keep transferring bitcoins among these wallets (my own wallets ) will that eventually consume all my coins (keep paying fees )?
We don't know whether the addresses belongs to you or not, the world doesn't know whether the addresses belongs to you or not because bitcoin has been designed this way.
It's anonymous and hence every address is unique. So yes every transaction will require a fee whether the address belongs to you or not.
So yes all your funds will be used when the transactions get mined and all your funds will eventually be split into miner rewards.