Electrum is an HD wallets which means all your keys (and addresses) are being generated from a single seed. you can use that seed or the extended key to re-generate all the addresses. some block explorers support extended keys. all you have to do is to give it your extended public key (starts with xpub) and the explorer generates all your public keys and addresses and returns their history.

warning
there is both privacy and security problems with doing this.
privacy issue is rather obvious since the explorer can now link ALL your current and future addresses that you use together.
security risk is that since Electrum is not using a hardened path, if a single private key of your wallet is leaked ALL your keys will be revealed and you can lose money.

a better solution is that you stick to using Electrum itself either through the client or if you insist on creating your own application then first generate your addresses from your extended public key locally in your own app and then using a loop through the list fetch their history from either an explorer or from any Electrum node using the Electrum communication protocol.