From an initial reading, it looks like your best long term option is to develop a database of all your information, and then use this to setup reports (per child, per group of children, etc) on key information. I could develop this for you, as well as key forms for entering data, and give you training on how to keep it updated. We can also discuss what insights you're hoping to gain, and how to grow it if your business grows.
I don't think you'd be best served at the moment with a mobile application as others are proposing. A database like I'm suggesting can be a Web application at a later stage, but it's best to start at the ground and build up rather than spend a lot of money developing a site and then have to work backwards if a change is needed.
If you accept my bid, we can discuss further. I work full time in data administration and analysis and have extensive experience in creating solutions from scratch, as well as training and support to people who may not be overly IT literate.