Being prior service with an RE3, am I eligible to join ROTC?

An RE3 re-up code is waiverable but will require CG of Cadet Command decision. Here is the verbiage from the Cadet Command pamphlet on contracting eligibility:
e. If the disqualifying RE code resulted from medical reasons, the applicant must clearly and completely state the reasons and produce an SF 88 and SF 93 stating the condition. Examining and reviewing physician statements must address the condition(s) that resulted in the disqualifying RE code. A copy of the disqualifying medical examination, or Medical Waiver Review Board results and current medical examination showing the condition no longer exits are also needed.

In terms of age, you are ineligible for a scholarship by US Code. However, you can still do ROTC as a non-scholarship cadet. Here is the verbiage from the same reference above:
(2) Maximum. Applicants must be young enough that they will not be 39 years old or older at the projected time of commissioning.
(3) Waivers. There is no longer a waiver requirement for Non-Scholarship Cadets thru the age of 34 year at the projected time of commissioning. The Brigade Commander is the waiver authority for applicants who will be between 35 and 39 years of age at the projected time of commissioning. Waivers must be approved prior to fully contracting the Cadet. See Chapter 3 for waiver processing procedures.
(4) Applicants who are to be appointed after their 39th birthday should be advised that they may not be able to qualify for retirement pay under 10 USC 1331, although they may be able to qualify for retirement pay under 10 USC 3911 if they have served on active duty for 20 years, at least 10 years of which have been served as a commissioned officer.

Finally, you start a new service obligation when you commission. Prior active duty time does count towards retirement time and time in service but does not change how long you will have to serve to meet your new obligation.

Let me know what other questions you have.

I’m prior service and I was told I had to graduate the December before my 32nd birthday in order to commission without a waiver. I believe the age of commissioning waiver is up to 39 based on the needs of the service. As others have mentioned, I believe your biggest hurdle will be DODMERB. I encourage you to reach out to a ROO and start the process

You can do college ROTC as a school elective. Issue is getting qualification for scholarship and/or commission. To become an officer, DODMERB physical is required. Doctor would have to assess your previous medical issue