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run SUS/PCC and re-install the latest software
Anytime, plus even if there was a Sony Xperia Care center at your country, it wouldn't be covered by Sony's warranty as it was bought at a different country.
That should be true but not if the phone is not sold in your country, if it is then there might be a company that is in charge of repairing Sony's phones.
You need to get it repaired