Hi BiancaArmellino,
welcome to the Apple (user-to-user) Community!
Re: How can I recover deleted messages on my MacBook Air?
Apple Support's online article : Delete messages and conversations in Messages on Mac - Apple Support
says how to:
"Recover a recently deleted message or conversation
When you delete a message or conversation, it’s moved to the Recently Deleted folder. You can view and recover items in the Recently Deleted folder for up to 30 days. After 30 days, the messages are removed from all your devices. After 40 days, the messages are permanently deleted from iCloud.
- In the Messages app
on your Mac, choose View > Recently Deleted. - If you don’t see Recently Deleted, you may not have deleted a conversation within the last 30 days.
- Select the conversation in the sidebar.
- Do one of the following:
- Recover a recently deleted message or conversation: Click Recover.
- Permanently delete a recently deleted message or conversation: Click Delete".
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Re: so I texted someone earlier from my MacBook Air and had a conversation with important info, but now when I open my Mac the convo is nowhere to be found
See how to: Search for a conversation in Messages on Mac - Apple Support
or
You may want to check or: Change iMessage settings in Messages on Mac - Apple Support
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If you still need help: Try quitting Messages app, and then open and sign back in ... check for the messages.
or
You may want to try re-starting your Mac : ie: Apple Menu > Restart (deletes temporary files, re-establishes connections, may update recent setting changes, often restores order if something is not working as expected.)
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If more support is needed:
Apple Messages Support Website
(Eg: online chat / phone / email etc. from the "Get Support - start now" link at the bottom of their webpage).
Messages for iPhone, iPad, Apple Watch, and Mac - Official Apple Support
All the best :-)