If the white gunge is inside the foreskin, this could be smegma and you need to pull back your foreskin and wash it gently.
As there is swelling and itching it may also be that you have a bacterial infection call Balanitis and you may need an antibiotic to treat this.
Because the area is dry, itchy with the white gunge, it is highly likely that you have a fungal infection.
Your doctor would be able to take a swab to find out if it is a fungal or bacterial infection. If it is a bacterial infection you will need a course of antibiotics.
If it is a fungal infection, you will need an anti-fungal cream to apply to the washed and dried penis. The doctor may prescribe an anti-fungal cream and/or antifungal oral medication. You can buy these things without a prescription at the pharmacy. If you speak with the pharmacist he will be able to advise you which medication would be suitable for you.
Best though is to go to the doctor and get a swab taken or go to the GUM clinic.
In the meantime, do not use normal soaps to wash your genitals. Only use soaps with the same pH levels as our skin. Wear cotton underwear and avoid manmade fabrics. Use latex free condoms in the event you may have an allergic reaction to the latex. Use non-biological washing detergents and fabric softeners that are suitable for people with allergies.
As a home remedy, after you have gently washed and gently dried your genitals you can apply natural set yogurt to the penis. You can apply this for as long as is required and it will cause no side effects.
Avoid having unprotected sex until you are well clear.
I agree with the above except yogurt used to be the home treatment prior to the anti-fungal medications going over the counter (OTC). By applying a moist paste-like yogurt to the affected area will only make the situation worse. You will want to consult your doctor and pharmacist first on the treatment.
Sorry to disagree. But in the event of not being able to get any antifungal medications (which can happen), natural set yogurt is a brilliant home care alternative - there are also no side effects from using yogurt.
None of the gentlemen that I know that have used the yogurt home remedy, have ever complained that it made their condition worse.
For emergency use yogurt is fine to alleviate any nasty discomfort in both men and women. But seeing a doctor with any genital problem to get a swab taken to identify the cause, should always be done if the yogurt does not settle the problem in a few days.
Using yogurt as anti invective home remedy is an excellent suggestion.