What doctor did you see? Your primary care physician or an OB/GYN?
Your PCP may have green lighted you but most OB/GYN's (my mother-in-law is an OB/GYN) won't do a tubal-ligation on someone your age unless it's deemed medically necessary because many young people who have it done change their mind later.
The procedure you're describing is more so a hysterectomy rather than a tuba-ligation. An OB/GYN is also unlikely to perform a hysterectomy on someone your age unless it is medically necessary. Having a (total) hysterectomy will put you into menopause. If you have chronic pain from PCOS or Endometriosis they may consider it as a relief of pain, but even then there's still pain because those are endocrine disorders and you still have an endocrine system with or without your ovaries.
You mentioned that your insurance is through a Catholic organization, most Catholic sponsored health insurance plans do not cover sterilization procedures for women or men. I've worked for a Catholic healthcare company that has hospitals all over the US for 10 years and not only does their employer sponsored medical insurance not cover sterilization procedures, their facilities do not perform them. The only time they will do a hysterectomy is if it's after a woman gives birth and they can't stop the bleeding, which makes it medically necessary because it's life threatening at that point (she can bleed to death). They also don't do vasectomy's. For any non-emergency & non life threatening sterilization procedures they will refer them to facilities that do.
How were you planning to get it done for free off of your mom's insurance? This isn't a free procedure, it still has to be paid for. If you don't have any insurance that covers it, you're responsible for 100% of the bill. Tubal-ligation procedures can cost $6,000.
You may or may not change your mind on being a parent. My best friend that I've been friends with since we were about 22, she didn't want kids and she's 44 now, that never changed for her. She's happy being a foster mom to dogs. Me, I wanted kids but I was indifferent on biological or adopting and I have both biological and adoptive kids. Another friend of mine did have hysterectomy at your age and then regretted because later in life she did want kids, she ended up having a baby using a surrogate.
If you eventually meet a partner who also does not want children and you're both sure of that a vasectomy is a lot less invasive than a tubal ligation with a lot less down time. Depending on how it's done, you can be sidelined anywhere from 3-6 weeks afterwards. My husband is also a physician (just a different kind than his mom) and when we decided our family was complete since after the birth of our last baby, he opted to have a vasectomy done. He went back to work 2 days later.