Sorry that I am just popping in and don't have time to read the other responses, so this may be a repeat!
Please speak with either the pediatrician to determine how many calories/fat/nutrients from fluids are required daily in lieu of breast milk, dairy milk or formula. It is dangerous to start an infant on a rice milk, even the enriched kind, in place of the above. It does not contain the correct nutrients required by a growing infant.
If possible, continue to nurse. You may have to limit the dairy in your diet. It depends on the mother and child, but some studies have detected dairy protein passed through breastmilk. If he will not take to the breast, pump as much as is needed and give it to him in a bottle or cup, mix with cereal, etc.
And if your child has a true allergy, please check with your allergist before starting any other kind of nut milks, such as almond!!
The Food Allergy and Anaphylaxis Network is a great resource. I believe it is www.foodallergy.org. Or google "FANN". Also, there are several parent-support groups in the Chicago area for parents of kids with allergies. You can google MOCHA (Northside), POCHA (Oak Park), POCA of DuPage to find out more.