Spots on hands from soap

Great question...however I don't have an answer.

I would suggest that you ask a dermatologist what they would recommend. Maybe calling their office would be sufficient without having to be seen.

Dove works fine. It worked before and now is no different. If you ask a doctor, they will tell you that we should not be using antibacterial soap. It only encourages the mutation of germs and viruses to more powerful strains that are harder to fight. (Same with antibiotics, by the way. The reason that doctors insist patients use all of their antibiotic is because stopping the antibiotic before you're 110% sure it has been cleared out of your system only creates antibiotic resistant strains of whatever you had.) But that's another subject. Sorry for going off on a tangent. Here's a direct quote from the Mayo Clinic:
Antibacterial soaps have become increasingly popular in recent years. However, these soaps are no more effective at killing germs than is regular soap. Using antibacterial soaps may lead to the development of bacteria that are resistant to the products' antimicrobial agents — making it even harder to kill these germs in the future.
The only things you need to worry about when washing your hands is this (another quote from the Mayo Clinic):
Wet your hands with warm, running water and apply liquid soap or use clean bar soap. Lather well.
Rub your hands vigorously together for at least 15 to 20 seconds.
Scrub all surfaces, including the backs of your hands, wrists, between your fingers and under your fingernails.
Rinse well.
Dry your hands with a clean or disposable towel.
Use a towel to turn off the faucet (if washing in a public bathroom.)