How to check that a sent text message has been read

There is no way to see that, if you are referring to an actual SMS text. An SMS does not show delivered or read. An iMessage can show delivered, and if the receiver has configured it, it can show read. If they do not configure the read receipt, then it will only show delivered.

SMS or iMessage? If SMS, there is likely no way to do that, but you would have to ask your carrier. If iMessage, you can get notified if someone has read your message, but only if the recipient chooses to share that information. They would have to go Settings > Messages > Send Read Receipts ON.

You're welcome.