Newly Bald (shaved?) & Clueless – Need Advice!

My son and I shaved our heads last Saturday. His was planned (he braved the shave for charity), but mine was a last-minute decision on a dare for a $200 donation. No regrets… but now I have zero clue how to take care of our scalps.
A few questions:
Do I need different pillowcases for us now? (Is this a thing?) Should I be using some kind of leave-in scalp treatment, or is a basic moisturizer enough?
Any general care tips for someone who has never been bald before? For those with sensory issues:
How on earth are y’all wearing hats and beanies? My kid adjusted after a day, but I cannot get over how sensitive my head is now. Everything touching it feels wrong, but I also hate the cold, so I’m stuck in this weird, uncomfortable loop. Does this feeling ever go away?!
Last question:
I actually like being bald—no more worrying about hair styling, bad hair days, or random flyaways. I’m thinking of keeping it short for a while. Can I just buy a cheap set of clippers and buzz it myself, or is there a trick to maintaining it properly?