Just to add, if you just wish to go completely offline, you do not have to use a block explorer like the one suggested above anytime you wish to check your balance, you can simply create a watch only wallet.
By the name, a watch only wallet only allows one to watch the wallet, but cannot be used to sign transactions. To set up;
• Download a reputable wallet software like electrum from the original website and verify the signature,
• Copy your xpub (master public key)
• import your wallet into electrum using the xpub
You can check your balance and previous transactions at anytime without your private key being online.
If you share a public key (aka Public address or wallet address) it is safe and there will be no threat of other people taking over your wallet.
The wallet address is a hash of the public key with some other components, they are not the exact same thing. Your public key is not revealed when receiving Bitcoins, but only when initiating a transaction.