Publish: It seems to take a long time for the email to arrive to the other person when sent through the email quick share

I assume you are referring our 'SHARE ON EMAIL' feature:

I tried to share my sample form with this feature. I was able to receive the e-mail immediately.

You can learn from these guides how to view your account email activity logs:

https://www.jotform.com/help/370-How-to-View-Your-Account-Activity-Logs

https://www.jotform.com/help/293-How-to-View-All-Your-Form-Email-History 

Please check again and share your form ID with us if the issue still persists? So, we can check the problem further.