When you pay through your nose for an object, what you are doing is paying too much for it. The expression is mostly used in informal contexts.
*Raju fell in love with the old car. He was willing to pay through his nose for it. *I had to pay through my nose for those tickets.
According to some scholars, the expression “pay through one’s nose” came into use when the Vikings ruled over much of Ireland between the Ninth and 10th Centuries. The rulers apparently levied a “nose tax” on the Irish. The people who did not pay the tax were punished by having their nose slit! The poor Irish were forced to pay a lot of money just to keep their nose intact!