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Sorry to hear this but you would need to either return your device to the place of purchase or contact Xperia care and have your device inspected in order to receive a price as we are members like yourself and are unable to offer prices as we simply don't know http://www.sonymobile.com/global-en/support/contact-us/
We are members like you and not Sony employed so we have no influence over Sony so as much as I can empathise with you I'm afraid we can't help in matters like this
I had the similar/same touch screen problem last month. Luckily, it was under warranty, so free repair.
It also took 1 week to repair, and I saw a very long parts list. I don't know what got changed inside, but the front panel and side frame got replaced. Repair center tested waterproof as well before returning it back to me.
Good service provided by service center staff overall.
I agree 1 week is way too long as smartphone has direct impact on a person's daily lifestyle nowadays. I hope Sony will learn from Apple ... exchange for a refurbished same model phone.
1 more thing ... Sony repair center staff needed to wipe the phone. I couldn't do a backup because there was no way to unlock the phone.
I hope you do backup frequently.