Another vote for Country Save with vinegar rinse. My childhood pediatrician who is still a good friend says she sees more skin problems from Tide than anything. It does not have enzymes or a number of other ingredients that coat and stay on the fabric.
So sorry you're dealing with this!
Lanolin is truly amazing, but yeah its sticky. We use Target brand Up and Up Sensitive wipes (purple package) that have lanolin.
You might skip the soap in the wipe solution, and only use it for poops. For us it breaks down the skins natural barrier too much. I also don't over wash at baths, using Cerave once a day and soap only if he pooped that day.
I LOVE using neti pot rinse packets (or 1/4 tsp each baking soda and sea salt) in 8 oz water for wipes. It's antibacterial, anti stink, and matches skin more closely than water (water itself can dry skin, lol).
We actually don't wipe at every change, either. With frequent changes it just wears skin down. Fresh urine from a healthy body is sterile and healing. Weird but true.