Is the proper phrasing "SMS" or "SMS Message"?

Solution 1:

First, there's nothing wrong with "ATM machine", "PIN number", or "scuba gear". The argument that they are redundant or erroneous is an example of the etymological fallacy, the argument that how a word originated tells us the "right" way to use it today. Acronyms are words and they develop meanings that are not necessarily identical to the meaning of the words from which they are formed.

You can use either "SMS" or "SMS message". The term "SMS" can refer to either the service itself or a message sent using that service.

Solution 2:

You can use SMS in place of SMS message if you wish.

Here's an example taken from Orange:

The first time you use this service you will receive an SMS with an invite to enter your twitter username and password.

Here's an "O2 guru" explaining "how to send an SMS".

In the UK, US and Australia most people call SMS messages text messages or texts, and sending SMS messages is called texting.

Solution 3:

Use "SMS message"; everyone does. I googled "SMS" message and SMS alone always refers to the messaging service, not to an individual message.

I don't think it is as redundant as PIN number or ATM machine, since a Short Messaging Service message is a message using that service, whereas PIN number, for instance, is redundant.