When I read your own thoughts going into your decision to redshirt, you gave very good reasons that he is not quite ready socially and emotionally and you sound very happy with your decision.
Others in your life mean well, but they are not his mom. They do not see everything you see. Your mom is from a different generation with a different reality of what kindergarten is (Kindergarten used to me much less academic.) and a different cutoff date (if any). When I was 5 the cutoff in Illinois was Dec 31st. Now it's Sept 1st. His pediatrician is a medical professional, not an educator. Your friend is being a good friend to your needs and letting you know that you could use a break. But the fact that she said he needs to be away from you makes me think that she would agree that he's not emotionally ready for kindergarten.
It bothers me when people say, "He's 5, so he should go." We all know of people in their 20's who think college is all about partying, while there are 15 and 16 year olds working very hard, hoping to earn scholarships. Age isn't everything!
It also bothers me when people say that he can always repeat kindergarten. While it's true, why would you want him to repeat anything. If you think he needs that extra year, give him that extra year with the kids he who will be in his class, his peers.
You know your son. His preschool teacher works with kids this age and knows (from experience) what kids need in order to succeed in kindergarten. If you want to listen to anyone, that's the one person I would choose.
We decided to redshirt our son. I talked to so many parents (whose kids where in middle school and high school). Some sent them when they were 5, others waited and sent them when they were 6. Of those who sent them when they were 5, many were very pleased with their decision, but many said, "I wish we would have waited." I have never heard anyone say, "I wish we would have sent him/her sooner." Many people who send their 5 year old with a later birthday say that everything was fine at first. It was when they were in 4th grade or middle school that their child really started struggling.
Your "Mommy Gut" told you he wasn't ready. It's completely normal for you to want the people in your life that you trust the most to think you are making the right decision. But you know him best, and you were already happy with your decision. Trust yourself.
ETA - Whether he thinks he's ready for kindergarten or not is completely irrelevant. He doesn't have a clue what kindergarten is. My 5 year old told me last March that he was ready for kindergarten. I was shocked. Where did this come from? He goes to daycare full-time, and during the school's spring break he noticed that none of the school-agers had to take a nap. He concluded Kindergarten = No Nap. He's no dummy, but he also wasn't in kindergarten yet. He is now, and so far, so good.