This is an idiom or expression mainly used in very informal English. To pay through your nose is to pay a heavy price for something.

If you want to fly during this festive season, you have to pay through the nose.

Getting that old car repaired was not a brilliant idea. I had to pay through the nose for it.

I had to pay through the nose for my sea-facing apartment in Mumbai.

If you want a gaming laptop with high end specifications, you have to pay through the nose for it.

The idiom cost an arm and a leg has a similar meaning.

Sports cars are highly desirable but unfortunately they cost an arm and a leg.

Sports cars may be highly desirable, but if you want one, you have to pay through your nose for it.

The expression pay through your nose has been in use for over ten centuries. According to scholars, the Danes had imposed heavy taxes on the Irish when they ruled Ireland. If an Irishman failed to pay the tax, they would cut his nose off. This practice eventually led to the formation of the phrase pay through the nose.