Hello,
The plus sign and 0011 prefix can be used interchangeably (either one or the other, never both). The same way when calling/texting from Mexico you can use either 00 or +.
Now, if the sms went through when you texted one Australian cell then it should normally go through for all Australian cell phones. The only possible issue could be that the other cell phones you texted are serviced by a different carrier than the one serving your girlfriend. Sometimes sms messages do not work internationally due to lack of agreements between carriers. I would say that this is unlikely in your case though. Calling your current Mexican carrier to inquire about this might help.
Since you have a Mexican mobile number now people from Australia should use the required dialing sequence for calling/texting a Mexican cell:
0011 52 1 xxx ??? ???? or + 52 1 xxx ??? ????. xxx is the city code where your phone is registered. 1 is a digit used when contacting Mexican cell phones from outside Mexico. See more info below:
https://www.howtocallabroad.com/results.php?callfrom=australia&callto=mexico