A week ago, I had washed my penis with a new soap. Unfortunately, a few hours later, I experienced a burning sensation on my glans, and saw some skin peeling. I immediately rushed to the shower and after that put on Vaseline. Now in the present, my glans seems to be flaky and itchy. There seems to be some light red spots on it as well, not sure if you can see it on the picture. Does this mean I have Balanitis or something?
it looks like your glans has had a bad reaction to the soap used. The skin of the glans is very thin and easily damaged so always only use warm water to clean and always dry thoroughly before putting the foreskin back in place. I’ve had the same in the past as you, usually the flaky skin goes away and the glans repairs but be patient, it takes time.
Darum, I fully agree with what James has detailed to you. Until the skin on the glans / head of your penis is back to normal, regard everything that the skin is in contact with as a ‘poison’ - so this is not only soap but ALL forms of body wash such as shower gel.
Draw your foreskin as far forward as you can when you take a shower, when you have cleaned and fully rinsed everywhere else on the body, expose the head of the penis and use the running water only to clean the penis with.
As James states, any time you wash the penis, and with water only of course, it must be completely dried with a clean dry towel that only you use. Do not be surprised if it takes 3, 4 or even 5 months or more for this to heal.
If you are sexually active or masturbate, I would suggest going without for around 3 months, or certainly until the skin look COMPLETELY normal again …