Did you confirm the address you copied from skype before hitting send. Just throwing this out there to doublecheck your system to ensure you didn't pick up any malware that replaces addresses, always best practice.

In the future a good practice is to copy the message and respond to them to confirm the address, this way you can definitely prove that you sent to the right address and no one can edit your reply.

Can you post your txid? At least this way some people can try and piece things together if there is anything to find and prove.