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 )?
That depends on how often you transfer and the amount of your coins.
It's costly to you if you keep transferring coins while you are not holding a decent amount, currently the transaction fee for transfer
is not a big amount, even exchanges could only charge
BTC 0.0005 and that is $2 or more but if will not affect you if you hold
thousand of dollars in your wallet. I'm sure with your personal wallet you don't have to pay that much.
Having different wallets can minimize the risk, but you can minimize fees also if you will manage your transfers properly.