No. vaseline may help moisturize the skin, but it will not cure it. There is no current cure for eczema, but there are other treatments and some work better than others.
Vitamins alone won't provide cure but will aid cure. Vitamin E
You can cure a dog's eczema by applying lavender oil and aloe to it's ears. Both of these products will help heal and rebuild the skin cells of the ear.
Maybe there should be trials conducted? Unfortunately I've no access to a horse.
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Try Vaseline, If you cannot get a prescription from the pediatrician.
Steroid ear drops. That is all I know of. Looking for more.
Unfortunately there is no 'cure' for eczema. To try and keep the skin as clear from eczema as possible is to moisturise on a daily basis (or as much as needed), and for any inflamed, red areas of skin, a corticosteroid cream may be prescribed by your doctor.
Not necessarily. If it's determined you have an allergy to cats and nothing else improves your symptoms however, than it is probably for the best.
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There is no cure for eczema, but it can be reduced. Definitely see your doctor, they may be able to refer you to a specialist. Keep using a mild moisturiser (such as E45) as much as possible and look out for dietary and environmental triggers for it. It might be worth trying an exclusion diet to attempt to identify causes. Some people get eczema when they are anemic; that might be worth checking. Something that may help alleviate the pain at times is an ointment called "Aquaphor". A good lotion to use after showers or baths is "Cetaphil".
Vaseline may help a little to fade stretch marks. The best use for Vaseline is to help prevent stretch marks before they form. Keeping skin moisturized is important in preventing stretch marks.