Longrest macro

If I'm not a GM in my game, can I set up the longrest macro for myself?

If the GM has set up an API script that will perform a long rest, probably. But more information is needed for a good answer. What sheet are you using, what API script does the GM use that would support it, and does the game even support the API (Pro user-created)? Also, you may need to ask GM permission. Chances are if they are running a script that allows this, they can give you more specific help.

He has not set up the API.  It was discussed, but now action was taken.  

If they install the "5th Edition OGL by Roll20 Companion" script (Assuming this is for the D&D 5th Edition by Roll20 Sheet), and you select your character token and run a Token Action: !longrest @{selected|character_name} that should do it.