The SBA instructor says their's this thing called an "Operating Agreement" that you have to document with the state as well, and that without that, the LLC you created does not mean jack squat even if its a Single-member LLC!!
Frankly, that doesn't sound right. In the states where I have practiced law, having an operating agreement is a good idea if there is more than one member, but isn't strictly necessary. However, they do things differently in Texas. The laws that govern LLCs are state laws and are different in every state. Perhaps Texas has a requirement that even a single member LLC needs an operating agreement. My guess is that a) the SBA instructor doesn't know what he/she is talking about or b) the SBA requires that any LLC that gets an SBA loan must have an operating agreement and the instructor misunderstood that.
Anyway, I don't represent you, so have your own attorney look into this for you. At the least, fire up the Google and see what "Texas LLC operating agreement requirements" turns up.