I've never seen a 4yo get immunotherapy via shots. They just don't tolerate to process well. If they have a lot of allergies as you described, it's likely to be two shots weekly for 4-6 months before they can be started to be spaced out. It can be a 2-4 year process. Even if the child could tolerate it, it is also a difficult thing for parents as you have to go to the doctor's office, get the shots, then wait there for 30 minutes to make sure there is no reaction.
As others have mentioned, SLIT is a better option for a 4yo but there are some things to consider. It does not work equally for all types of environmental allergies. All immunotherapy is poor for cat and dog dander. If you have an animal that your child is allergic to, you are going to have to get rid of the animal. If there is a significant dust mite allergy, get rid of your carpet and get encasements for the bed and pillow. Get rid of stuffed animals. SLIT works best for grass, weed, tree type allergies. You're more likely to see improvement if those are the things that tested positive.
No material on this site is intended to be a substitute for professional medical advice, diagnosis or treatment. See full
Medical Disclaimer.