What you are looking for is studio management software. They can do what you described, but also much much more. They help with things like invoicing, calendar scheduling, relationship tracking, referral tracking, billing, etc.
The pieces that you outline only really fall under relationship tracking, so many of the full solutions might be overkill for you currently, but as you grow into the business already having your data available and in a system like this may benefit you and help you to grow faster/easier.
Some examples of this software include, but are not at all limited to:
- Studio Cloud
- ShootQ
- TaveStudioPlus
- PixifiPixifi
- StudioPlusTave
- GenBookStudio Cloud
- GenBook