Where to look
Settings → Notifications → History lists each message with the recipient, what it was, when it went out, and whether it was delivered.
Per appointment and per client
The same messages appear on the appointment's activity and on the client's timeline, so you can answer "was I reminded?" without leaving the record.
If something did not arrive
Check the address or number is right, ask the customer to look in spam, and confirm the message is turned on in your notification settings.