For recovering the deleted messages from instagram it is not possible because instagram is not support that but you can try these some methods to recover:
1.Login to your instagram profile.
2.Then go to the setting >security>download data.
3.Then request your data, which includes some messages.
4.After Doing these wait for the email with download link
5.When mail comes to check the deleted messages are came or not.
If this method does not work you can check the archive section because sometimes the message is not deleted but it goes in the archive and stores there.
For more info : https://techyvibe.net/how-to-see-deleted-messages-on-instagram/