Rude? Not sure. Blunt, yes.
“Could you pick me up at 4:45?”
OR
“Is it possible you pick me up by 4:45?”
…would have been fine.
Even if please is not written, there were two things wrong here,
1- It was not a request and sounds like an order or blunt statement.
2- Adding statement of time limit (15 min) was not a good idea when asking anyone for a favor.
No matter how good relation is, it is always safe to add few words to make other person glad to do favor in relaxed manner.
Anyhow making a big deal of it depends how the other person took it and in what mood and all of it depends what kind of relation two people have. With a good relation going, other person could have ignored the bluntness of the statement.
I know when sending a text message we don’t think of some formalities or spellings and just want the message across.