Hi @w1sey, welcome to our forum and I'm sorry to hear about what has happened to your Xperia X Compact. 
As this is a Global user based forum and the cost for repairs may vary between markets, I recommend that you get in touch with your Local support team and see if they are able to provide you with an estimated cost of a screen repair.
If you want, you can also write which country you are from and if another user from the same country have had their screen repaired they can tell you how much they paid.
I hope that helps! 
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