What are the visible effects of an allergic reaction to desitin in a ten month old baby?

Sounds like your little one is one in a million that may be allergic to zinc oxide which is a mineral. It could be cod liver oil or something else. I copied the following;
What is the most important information I should know about Desitin (zinc oxide (topical))?
Do not use this medication if you are allergic to zinc, dimethicone, lanolin, cod liver oil, petroleum jelly, parabens, mineral oil, or wax.
Zinc oxide topical will not treat a bacterial or fungal infection. Call your doctor if you have any signs of infection such as redness and warmth or oozing skin lesions.

Keep the diaper area clean and dry to prevent worsening of skin rash. Change wet diapers as soon as possible. Allow the skin to dry thoroughly before putting on a fresh diaper.

Stop using this medication and call your doctor if your condition does not improve within 7 days of treatment.
Avoid getting this medication in your mouth or eyes. If it does get into any of these areas, rinse with water right away. Do not use zinc oxide topical on deep skin wounds or severe burns. Get medical attention for more severe skin irritation or injury.
Avoid applying other skin medications on the same treatment area with zinc oxide, unless your doctor has told you to.
I would advise to watch this little one for other allergies too, & but call your doctor please...

When my kids were little one of the two boys had bad diaper rash and was really sensitive to diaper wipes. The pediatrician had me mix up a teaspoon of baking soda in a spray bottle of water to wash his diaper area with instead of wipes using a soft absorbent towel to wipe the mess away then spray again and let air dry. The baking soda helps neutralize the urine and feces and soothes the skin. We also used a powder that is in a pink bottle with a blue oval that had the name in it in white letters. I'm trying to remember the name-my kids are 20 and 16 now-I want to say Cal-something. Any way if they still carry that powder you cant miss it. I used to get it at Walgreens drug stores. Even corn starch powder will help but that other powder had an antifungal agent in it I want to say. I wish I could remember the name for you, it was good stuff! Using the baking soda water really helped clear their behinds right up! Good Luck to you! Poor baby-it sounds painful!!