Shin splints came back after 3 weeks off

They can sometimes take a long time to go away completely, cut back on the amount of distance you're running, try to run on softer surfaces, make sure your shoes are providing enough cushion, do some strength training (hips, ankles, quads, glutes, calves etc) and cross train until you can work your mileage back up. Sometimes icing is helpful if they're really painful, but I've heard it can actually prolong things so idk. Could also try taking more and smaller steps with shorter strides.

Not a doctor, but my understanding is shin splints are essentially a muscle issue, and there are workouts you can do to strenghten them that usually help me. Things like rotating foot clockwise 10x, counter cw 10x, and then drawing out the alphabet with your foot, while trying to put stress on your shin area.

Do every night and I'm usually fine after a week or so of this.

A barefoot cooldown pretty much always made my shin splints go away for a bit. Don't do a workout or 3 miles or something barefoot out of nowhere, but doing a cooldown barefoot may help a lot. It strengthens/uses muscles that don't get used as much with shoes on, and can improve your form, which both help with shin splints. At the most, I do 10-15% of my mileage barefoot, and I think it helps keep me healthy.

Shin splints signal a weakness. In addition to taking time off, you need to get stronger. Find a PT to give you guidance on exercises, surf the YouTube, or maybe get lucky with some advice here. I suffered from shin splints for 20 years (wish they had social media in my day), before I finally met a smart dude who told me and showed me how to build my lower leg strength. No problems for 15 years now.

What did the smart dude teach you?