You license has been suspended under Transportation Code Sec. 524.012 for a period specified in Sec. 524.022(b)(1). Its obvious to me that this is the case because I'm pretty sure there is no other two month suspension related to minors or DUIs. This section deals with license suspensions related to either refusal of the chemical test or failing of the chemical test. (Failing for DUI means that there is ANY detectable measure of alcohol.)
It sounds like the officer went ahead and filed his complaint (citation) with the court without issuing you a copy of the citation and without taking you into custody. This isn't exactly proper police work but there is nothing unlawful about it. If an officer has probable cause for the offense they can always just file a complaint and have the court issue a summons or just file for a warrant. This means that there is likely an open DUI case against you and you will either get notice of a court date in the mail, or you may have a warrant out.
The officer was required under Transportation Code 524.011 to confiscate your driver's license and issue you a temporary driving permit if he was going to file the case. The fact that he did not do this likely means that, for whatever reason, he was initially going to just let you off and changed his mind after the fact. Again, its sloppy but still permissible. Even though the officer failed to comply with 524.011, DPS can still suspend your license they just cannot consider the results of any chemical test against you as evidence, but there wasn't a test done anyway in your case. Take a look at Sec. 524.012 to see what I mean.
Here's where it gets a little bit tricky since you say you were never offered a chemical test. My strong suspicion is that the officer just marked down that you refused the test. This would certainly be all that DPS would need to issue this suspension. If the officer never offered you a test, and stated such in his report, then there are no grounds for DPS to suspend the license, but that doesn't mean they didn't do it anyway. DPS is a machine and I have seen them issue false suspensions time and time again. You need to get a copy of the officer's report to see whether he called this a refusal or not.
You don't have a right to a hearing on the suspension until after the suspension is actually issued and you get notice of it. Your timeline starts running on the fifth day after the notice is postmarked, and you have fifteen days to file for the hearing. Sec. 524.013.
If this period hasn't already expired you need to contact an attorney asap and have them file the paperwork and handle the hearing. They may be able to prevent the suspension. The requesting of the hearing also tolls the suspension.
If you are ultimately convicted of the DUI then there is a separate license suspension of either six months or one year. It is possible to have this initial two month suspension (if it sticks) count against this second suspension.
Yes it is possible to receive a probated sentence on a DUI and then get it expunged under Code of Criminal Procedure 55.01. An alcohol awareness class has nothing to do with the expungment but it is a common condition of any DUI probation. The court may also offer some form of pre-trial diversion program similar to a probation but which results in the charges never being formally filed. Technically under 55.01 you are supposed to wait until the statute of limitations runs before seeking an expunction and for even a class C that is two years, not one. This entire statute, however, is very poorly written as it applies to Class C offenses because they amended it to allow expunctions for probated class C offenses (previously could only seal them) without explaining whether the other two expunction requirements apply to Class C's or not. There are several different widely published legal articles questioning whether the SOL must run on a Class C before it can be expunged. The result is that most courts simply don't care and will readily ex parte grant the expunction, sometimes even immediately after you complete your probation. Again, just hire an attorney that handles expunctions and see how it works in your jurisdiction.