Obviously, it depends on your smartphone. Some cheaper smartphones don’t even have enough memory for your pictures or your music. But in general, most smartphones have enough memory to store all of your important health information, i.e. your allergies, medication, medical history, consultations...
There are 2 types of data that will probably not fit on your smartphone:
- a large number of high resolution images
- an extremely high number of parameters (like your blood pressure measured every few minutes for years)
There is not much that can be done for these 2 types of data today. We can only wait for higher capacity smartphones, which will probably come sooner than we expect.
The important thing to remember is that most smartphones have enough memory to store all of your important health information.