SMS reminder: twilio not working

Hi,
I want to install the twilio SMS, to send reminders to my customers 24hrs prior to the appointment.
I created an account with Twilio and verified my personal mobile phone number.
Copied the Account SID and Authtoken into the plugin. Entered my personal mobile phone number (+316XXXXXXXX), set up the other stuff, but I’m not receiving any SMS messages.
I did not buy a Twilio phone number as this would result in monthly costs and according to your description it is not necessary.

Any idea what’s going wrong?

Petra