PI is a class C misdemeanor, so it isn't very serious to begin with, but you can't be convicted for public intoxication inside your own home. Not even in Texas. Maybe your front yard, but never inside the home. There is therfore no probable cause for the arrest, and you should attack the charge on that basis. If probable cause is erroneously found, then you'll have to fight it out. The court has no authority to dismiss a criminal case absent a request from the State, but it sounds like this one should be an easy case to beat at trial. If you really want to be a pain in the butt, you should demand a trial by jury. In Texas, you have that right no matter what the charge is. Jury trials are very expensive and time consuming for the State. You may even have a civil cause of action against the police officers for false arrest, if it turns out that they lacked probable cause.
Now, as for the abuse of the 911 service, it sounds to me that you weren't charged with that. If not, then you should do ok. If you were, the State might have a case, depending on just how aggregious the situation was. Really, you should have just called the police instead of 911, if all you had to report was a friend comitting a criminal trespass by refusing to leave your house.
