Solid or gel or roll-on types tend to be the best for most parts of the body. Spray types can be more useful for the feet.
A deodorant is a product that masks unpleasant smells, often with a stronger smell of its own so is more like a perfume.
An antiperspirant is a product that contains a substance such as aluminium chloride that actively reduces sweating.
If the skin is wet then it will cause irritation.
Make sure that you follow the instructions from your GP and the instructions on the product.
If the skin has been shaved, leave at least two days before applying antiperspirant.
Sometimes an application of an emollient cream or 1% hydrocortisone cream to the area once the antiperspirant has been washed off can help.
It might be worth trying another type of antiperspirant or one that is developed specifically for the part of the body you are using it on such as SweatStop.
If you still find that antiperspirants do not work for you, ask you GP to be referred to a dermatologist.