Hi,
Welcome back to icliniq.com.
You are right. The low immunity is due to infection and lack of breastfeeding.
Just keep in mind that homeopathic medicines or treatment is not like allopathic treatment where you give a remedy only to treat the cold or a cough. In order to develop his immunity it is very important to understand your child as a person, as every child is different in terms of behavior, likes, dislikes, reaction to life circumstances, etc. The homeopathic remedy is prescribed and based on these features which not only would help to develop immunity but will help to fight and tackle the situations like infection, emotional stress, and physical stress.
Dr. Reckweg R 88 (Caryophyllus Aromaticus D3, Coxsackie D30, D60, D200, Diphterinum D30, D60, D200) will act only for a short period of time and also you cannot give this remedy for a longer period of time. This medication is only good for quick relief. You can give this as a preventive remedy but avoid giving it every day. You can give five drops of this remedy for a week then stop the remedy for the next three weeks and start again for a week. It means this medication can be taken once a month for a week. If you feel he is doing great, and the frequency of cold and cough has reduced drastically, then stop the medication. Similarly, Eupatorium can be taken for a week in a month. If he develops a cold or a cough, then you can give him Eupatorium till you see the improvement. Also, avoid giving him heavy and frequent doses of antibiotics or anti-viral allopathic medications as these medications will lower his immunity more.
In short, you can give him Rechweg drops for a few days but not continuously. If he falls sick due to any reason and if not feeling better with these medications, it is advisable to immediately seek professional help either from a Homeopath or any other physician.