But the private key which I had for my address in bitcoin core shows a different address in blockchain and I'm not able to see my balance.
Could anyone help or suggest me on this?
first of all, what kind of addresses you have in bitcoin core?
if
bech32 address then you shouldn't be using bc.info, they haven't fully supported native segwit address yet
if
1xx legacy address, it would be simple different formats display
it's a matter of compressed/uncompressed bitcoin address and private keys. what's your private key starts with?
starts with
5 for uncompressed address and starts with
K or
L for compressed address