Other people have already pointed out that your "problem" is very probably the blockchain congestion at this time (maybe a lot of profit taking after the bounce yesterday ...).
But if you are really concerned about blockchain.info being a "scam" and want to access your private keys, you can do the following:
- First locate the address from which you sent the payment.
- If it's an imported address, you can download the compressed private key for this address at the following link:
https://blockchain.info/wallet/#/settings/addresses . Go to the address, click on "More options -> Private key". If the client you want to use doesn't understand the two formats in which it is offered (WIF/base58) then follow
these steps.
- If it's an address of your main blockchain.info wallet, it's a bit more complicated: You must first locate/remember the "recovery phrase" you entered there to generate all your addresses. Then, using a BIP39 generator you can generate the private key of the address(es) you need.
Fortunately there is a tutorial available
here. Please follow it carefully and really
download the BIP39 generator - even if the page seems to be secure.