I added reminder as a custom filed so that when I create an issue I set the reminder, but I do not get the reminder throw the email
When viewing issue reminder is displayed on the right of the issue. When you hover on it it should show reminder targets. Please check it is correctly set.
I check it and it is correct, whatever I assign it to myself but I do not get any email, does it look at the user profile and pick the email from there?
Yes, I gets email from your user profile. Also your Jira instance should able to send email to specified email address. Sometimes jira instances are not allowed to send email outside of Intranet.
We can check whether email are send or not using logs. If you turn on logging as explained here, you can see why emails are sent or not sent.