If you have control over the PHP code that handles the changes over mysql, you can write your trigger in that code itself, If you only have access the MySQL db not the code that writes to it, you should create a trigger for that particular table, and on change, write some row to another table.
This way you can write a different PHP script that checks the other table in a cronjob for example, and send you an SMS, If some new rows inserted to that table, using Twilio API or another SMS gateway since they do not matter.
See MySQL Trigger Documentation for more information