You'll need to contact the carrier and request them to resend them to you.
Carriers keep copies of every message sent and received for legal purposes. Ie, the police suspect the phone has been being used for drug trafficking. They would then get a warrant and the carriers would give them logs of the messages so that they could inspect them for incriminating details.
It's not like there's someone there at Verizon (or whatever carrier you're with) reading your messages all day long to see what you're up to. They're simply logged in their servers for a reason like the one above.
If you can verify your identity and ownership of the device, call the carrier. They will help you.