Web database program

I currently have a handibase database that works well on my pdf to keep track of pregnant clients. I would like to have a similar secure database online, on my server, that could be updated and viewed remotely, including on iPhone (views must be compatable). There would be approximately 15 fields, some including date calculations, that would have to be updated each time based on current date; each field can be separately sorted; a sort feature that allows one to exclude only data meeting that specification. As an example a typical entry would consist of Name, date of birth, age (calculated), due date, current gestational age (calculated from due date and current date), several drop down date entries, and several tick boxes (that would enable the user to easily exclude or include these variables in search criteria), date of delivery, and a few other variables. As an example, one should be able to list all clients by name (alphabetically), sort by due date or current gestational age, exclude those who have delivered, include only those who delivered between such and such dates, etc.