Will you automatically upgrade...

me to the next level when I reach one of the limits?

Hello,

While automatic renewal of the existing plan is possible (and that is how the payment process works) - automatic upgrade of plan is not possible.

You will need to manually upgrade the account when you reach your limits.

You can keep a tab on your account usage from your Account Settings > Usage page: https://www.jotform.com/myaccount/usage 

Here is a related guide for reference: How-to-Upgrade-My-Account