If not, I would like to know if there is a way to check the balance of an address using the btc network and not a blockchain explorer, for example with some node calls running btc core.
You can create a watch-only wallet in electrum just using your address.
If you want anonymity while using blockchain explorer, you can use Tor browser to check the address or addresses that you want which is better than using Electrum that connects using IP address, or enable Tor with Electrum for it.
For privacy, you have to run your own node.