I don't need to look at the pictures.
You MUST go and see a doctor as soon as possible.
What you have has nothing to do with masturbation.
The Vaseline would not have caused the condition, but I don't know what type of oil you used.
With what you describe, you cannot treat this at home by yourself.
I suggest you do not use any soaps or shower gels when you wash down below. Just use plain water.
As a home remedy you can put on set plain yogurt after you wash and dry your penis, this will feel very cold and may help to ease the burning sensations. This will not cure your condition.
Applying the Vaseline will help with the cracking skin. But you may need antibiotics or an antifungal medication, or both, depending on the doctor's diagnosis. Antifungal medications come in capsule form to take by mouth and you can also get antifungal creams.
If you use condoms, only get latex free ones. Avoid sex until you are properly healed.
You need to get checked out as soon as possible, because the medication to be used will depend on the diagnosis.
You MUST see a doctor or go and get checked out at a sex clinic as soon as possible.
Sometimes a pharmacist is very helpful.