From the symptoms you are describing you are right to query an allergy of some sort. It is hard to tell if milk is the culprit without assessing the child, however in small children milk is often a common alergen. If there is a family history of asthma, eczema, allergy or intolerance your son’s chance of having an allergy is also increased.
The use of antibiotics unfortunately may have compounded your son’s problem. In children and adults antibiotics have the unfortunate side effect of destroying some of the beneficial bacteria that survive and populate the digestive system. These play a large part in the overall immune response and the integrity of the digestive system. The situation you have described is able to be treated and your son can be returned to a state of health, however this is best done under the care of a skilled professional who can consider the many aspects of your son’s case.
I have included some general recommendations you may wish to implement before you visit a Naturopath or children's allergy specialist.
Formula: There are a wide range of formulas available which are dairy free. These can include Goats milk formulas, rice based formulas and soy based formulas. If you are breast feeding you may wish to investigate if there are any triggers in your diet which may worsen your son’s symptoms.
Beneficial Bacteria: I would suggest the initiation of a bacteria supplement for your child to replenish the bacteria which has been lost through antibiotic use. Good products to use include Bioceuticals Baby Biotic. You may also wish to include an adult’s probiotic in your own daily routine. You will then pass this beneficial bacteria through to your child when breast feeding. Suitable products include Inner Health Dairy Free and Synbac.
Additives: If you are feeding your child solids, avoid food which contains any additives, colourings or flavourings which are not natural. Keeping food simple and non-reactive will also help you to identify any possible triggers.
There are herbal and homeopathic remedies that are suitable for children who display cold and flu symptoms and these are often beneficial when used in the early stages of illness, and may help to avoid the need for antibiotic treatment.