Why am I not allowed to go to the promotion board for being on profile for a pending surgery? Is there a regulation supporting my position?

There is a registration, it's called Enlisted Promotions and Reductions AR 600-8-19.
Read it and you will see when you are eligible to go and when you are required to go

Here's the thing.....you are on a temporary profile. Even if you did go to the board and get your P, you can't go to PME school with a temporary profile. Also, most Army units are being ordered to NOT hold an in person promotion board due to the spread of COVID-19. Also, the Army is stopping movement. Which means, no one is going anywhere any time soon. In order to go to school, you need a current/valid APFT score. You can't get that with a temporary profile. If you can't get to school due to surgery and due to COVID-19, you could very well fall off the PPRL. Perhaps your Platoon Sergeant is looking out for your well being and not wanting to waste everyone's (to include your) time. Have you sat down with your Platoon Sergeant and/or TL and/or SL to be counselled as to why you are not getting to the promotion board?

And food for thought, I once sat as a SPC for 11 years before making SGT.

You just need to tough it out and do what you have to do to get promoted the surgery will come. I went my last 16 years in the Army with no ACL, Went to BNCOC, ANCOC, AudiMurphy, Drill Sergeant School, two years on the Trail and WOCS and two Warrant Officer Basic Courses like that. A permanent profile want hurt you. I ran on my PT test and won every other award in school but it's all heart buddy. I was Artillery where everything was a competition so you don't want to fall behind three others. With that being said in year 20 I had a total knee replacement but it was worth all I put my body through.