This is exactly what I wanted to test: to see if the server spawns this error automatically or if it is a problem from your side.
And unfortunately, the problem is from your side. You have over 12.000 rows in
messages table. Each time you browse the chat your script does a lot of queries to retrieve the messages registered in your database: one or more queries per message -- this depends on how you have coded your chat as well.
I suggest your to take a look on how you have coded your scripts. Try to minimize the number of queries. Or else, please consider buying a paid plan, which does not have such limitations: