Would an arrest for a class "C" misdemeanor be in my record?

A misdemeanor would become a part of your permanent record.  However, there is a process available, in limited situations, that will allow a person to clear their record.  It is called "expungement".

You may be eligiblele for expungement if:

• A criminal charge against you has been dismissed, you have been found not guilty, or you have been pardoned; or
• Someone used your name or identification when arrested (identity theft); or
• You are a juvenile who has completed a deferred sentence; or
• You are an underage drinking first offender.

If you are eligible to have your records expunged, you may file a petition in court.  In addition, if you have received a discharge and dismissal from deferred adjudication community supervision (an alternative sentencing program in Texas), you may petition the court for a nondisclosure order following dismissal for some misdemeanors, five years after dismissal for other misdemeanors, or 10 years after dismissal for felonies. A nondisclosure order prohibits criminal justice agencies from disclosing criminal history information to the public.

Again, this is just a limited procedure.  It may not apply to your case.  At this point, you should consult with  local attorney to see if there is any other remedy available to you.