Can't find messages that I saw come in!

Sounds like the message came in from a contact that you have Pinned on the top of the message list. With a Pinned message, you will see a blue dot on the pinned conversation and can tap on it to read the messages, but it will not appear in the list below. Here you can see what the Pinned conversations look like on the top of your Message list:

For more info on how to pin/unpin conversations, here is a support article that may help:

Use Messages on your iPhone or iPad - Apple Support