SQL injection is an attack against servers, what you are describing sounds more like XSS or clickjacking. Did you visit your exchange from google or from your bookmarks? Also, what happened next with your account, did you withdraw your money or are they still there?
No, I did not visit the exchange through Google, I always type the URL for my exchange, to make sure I access the correct site. I managed to Sell some bitcoins via another computer that did not do this, so this is why I am thinking that the browser might be infected. <Did this, after I posted this question>
Well, people should check the URL address after they clicked on options within the site, to make sure that they are not re-directed to other sites, after they logged into their exchange.