Okay, everything was fine and looked nice until I tried to book an appointment.

It's fair to expect the person making the booking to create an account.

However, to expect the receiving party of the booking request to also sign up for account is asking for too much and is unlikely to happen.

Also, why do you ask for people's contact details (address, phone, ...). Do you really need that info?. If anything just put the necessary stuff on the create an account form and put the rest of the info on a profile page that people can edit later.