Hi Anastasiya,
Thanks for checking out our plugins!
Both the The Events Calendar and Events Calendar Pro offer lists of events (Pro has more options for events lists), but unfortunately neither one is set up to handle appointments.
The closest we have to this functionality would be using The Events Calendar in conjunction with our free Event Tickets plugin, which allows users to RSVP to events that you create (or our premium Event Tickets Plus plugin if users need to pay to schedule appointments). You could set the maximum number of RSVPs allowed to 1.
Depending on your specific needs, this might work for you. I would recommend downloading the Event Tickets plugin and giving it a shot!
I’m sorry I couldn’t give you a better answer, but please let me know if you have any more questions, and I will be happy to help!