You can copy paste your address into the search bar in the link to view the balance.
https://blockchain.info/
However, bear in mind that if the exchange provided you with that address, it is likely you do not have the private key -
they do.
If you do not have sole access to the private key, then you are not in control of your bitcoins -
they are.
You will only know if you
can access your bitcoins when you request them to be moved to a wallet not under their control.
when if they go bust, get hacked or do a runner, your bitcoins will be gone with them.
You may not need to panic. They may be a "safe" exchange.
Do you know if you have a private key? (never show that key to anyone) Or just a send address (public key - can be shown)
Have you looked into using a different wallet to send your bitcoins too?