You have raised 2 issues regarding the health of your child. I shall address them one by one.1.Respiratory tract infections are very common in young children specially around 3-4 years of age. At this age the child starts going to school and comes in contact with many children. This increases their exposure to various viruses. The tendency to recurrent infections subsides over the next 1-2 years as the child acquires immunity. Most episodes of viral infection last for 3-7 days. However, some cough may remain for some more time. Sometimes a child may get re-infected by another virus and it appears as if the same episode is continuing. However, if your child is having persistent cough for 1.5 months, she merits a thorough evaluation including an x-ray chest, and some other tests including Mantoux test, blood tests, etc. There are many conditions that can be responsible for this situation and they need to be looked for. Avoid self medication and have your child evaluated by a paediatrician.
2. It is unfortunate that your child had to loose one kidney at a young age. However, I assure you that one healthy kidney is totally capable of handling the work of both. So your child is unlikely to have any problems. In fact in
some individuals, one kidney may be absent since birth! I am sure the function of the other kidney would have been evaluated before the decision to remove one kidney was taken. If its structure and function was found to be normal at that time, it is expected to remain normal. However noting your concern I see no harm in recommending a yearly ultrasound, blood pressure recording and urine routine examination. These tests do not involve any discomfort to the child and are not expensive either. Their results should reassure you.