I think my kid has an allergy to our dog and I'm at my wit's end about what to do. I can't get rid of the dog nor can I leave my kid suffering. He itches and sneezes a LOT. Will that help if the dog's hair is trimmed to the shortest? Do you have any other tips please? I really don't know what to do.
Trimming the hair won't help, as dander and allergens come from their skin. You could get your son allergy medication. There isn't a lot you can do other than that!
The allergens come from saliva and are then transmitted to the dog's skin&hair and then everywhere in the house. If you trim the dog it may help to some extent but the problem won't go away that easily. You may want to try dandruff reduction products and clean the house more often than you'd normally do. Also don't let the dog into the kid's room if that's possible. If your dog has fleas you'll want to get rid of them because fleas, mites, ticks and the like make the animal scratch more, which increases the amount of allergens in the air.
In addition to what has been said, you shouldn't only focus on the dog. You should also focus on improving your son's health. Allergies don't usually come as a sole problem. Improving his health and reducing other allergies if they exist should as well help with the dog allergy.

I'm glad you aren't going to get rid of the dog! Many people do that because it's the easiest solution but it's totally unfair to the animal.
Keep both of them and talk it out with someone who has been.in this situation
Claritin works really well. There are some products that you can use on your dog to reduce the amount of dander on its fur. I also think it would be a good idea to get a battery of allergy tests done for your child, as well as looking into immunotherapy sessions that would help alleviate symptoms. It takes quite a few sessions, but will provide relief for extended periods of time. Contact an allergist in your area to learn more about the details as they pertain to your particular situation.