Allergic reactions to pets are caused by proteins that the animals carry in their dander, saliva, and urine. Getting a hairless pet does not necessarily mean you're getting a lower allergen load, because it's not just hair or fur that's the problem.
Specific people can react differently to specific animals. This is where it gets tricky. It is possible to get specific allergy tests from your doctor, but harder although not impossible to get animals tested for specific proteins. Some breeders will test kittens or puppies for you before you purchase them.
It can be a decent strategy to spend time alone with one pet at a time before you adopt them, and see how you react. This can be difficult at a shelter, but sometimes the staff can help you get into a clean room with one animal at a time.
It is possible to live with a pet even though you react, depending on the severity of your reactions. Here are some tips for reducing reactions:
Choose carpet-free flooring, or shampoo your carpet frequently.
Use a HEPA air filter to remove dander and protein particles from the air.
Keep your pet out of your bedroom, because you spend the most time there. You might also consider an indoor/outdoor situation if appropriate. (Keep in mind there are pros and cons to keeping a pet outside.)
Bathe your pet weekly to reduce the amount of dander they release.
Consider "hypoallergenic" breeds. There is no truly hypoallergenic cat or dog, but some have less of the pesky proteins in question, or shed less.
Some herbal formulas or homeopathic remedies can help your body deal with allergies more efficiently. Remember, even over the counter natural products are best recommended by a trained professional. That's the best way to get something that works for your body specifically, and to avoid something that might not. Essential oils can also help symptoms, but likely won't fix the problem. Antihistamines are another option, but it's best not to rely on them entirely. Most professionals would recommend also doing environmental control like cleaning and having an air filter.