Educational Delay is really only relevant if you intend to apply and are accepted for active duty. If you take the NG/Reserve option you have to work out BOLC dates to not interfere with graduate school.
Ed Delays are not limited to Medicine and Law. However, they are limited to degrees needed by the Army. Your best source for the process and
'chances' will be cadre when you get to your school.
Here is the regulation - but understand the criteria may be more rigid/limited when it's time to apply late jr year/early sr year.
Use the search feature looking for threads on Ed Delay. They have links to the specific Ed Delay #'s and degree programs for recent years. As a % very few ROTC graduates receive Educational Delay. @AROTC-dad
might help finding the relevant links.