Sharing same account, effectively he has as much right to make purchase if you had the credit card details stored. Technically, you SHOULD NOT have shared the account but that's entirely another issue.

As far as to SE, it is a purchase made from the account and you "may" be able to ask for refund but I won't say or tell them that the purchase was made by your brother without your approval. Ask for refund on the ground that you "changed your mind" - if that's possible. You may want to contact your credit card company to say the purchase was made without your authorisation to reverse the charge should the process with SE isn't working.

Good luck.