( I don't want to import the private key into a wallet and just I want to check my balance)
use this bitcoin gold block explorer: https://btgexplorer.com
i just checked with my bitcoin address and it works. you just paste your bitcoin address in its search bar and it automatically converts your BTG address to BTG address and also shows you your balance.
one of the issues that these kinds of fork cause is that people send coins to wrong addresses. for example sending BTC to BCH address or vice versa. that causes a lot of headache for recovering your funds. you may even lose it if the address belonged to a service like a gambling site for example. they won't credit you back.
so they change the format so that BTG address is invalid in BTC and BTC is invalid in BTG. it is just the address format though, nothing changed about private keys.