I was charged with public intoxication but would it be better for me if I had been charged with MIC? 

Under Texas law, unlike in most states, it is against the law to be drunk, regardless of where you are or what you’re doing.  You don’t have to be driving, fighting, or causing any other problems in order to be cited for "Public Intoxication".  And unlike drunk driving laws, this PI law doesn’t define what constitutes being drunk.  Whether a person is or is not intoxicated is based on the officer's judgment; no field sobriety tests or breathalyzer must be administered.

The following is an excerpt from the Public Intoxication Statute of Texas:

Under 49.02 "Public Intoxication" the phrase "Public Intoxication" means:

"A person commits an offense if the person appears in a public place while intoxicated to the degree that the person may endanger the person or another."

"Intoxicated" is defined as: not having the normal use of mental or physical faculties by reason of the introduction of alcohol, controlled substance, a drug, a dangerous drug, a combination of two or more of those substances, or any other substance into the body; or having an alcohol concentration of 0.08 or more.

As to what "endanger" means is not clear.  The term is vague, at best.  However, the fact that you were asleep in a car would seem to negate that you were any kind of danger to either yourself or the driver.  Your next step should be to consult with an attorney in your area on all of this (depending on your finances, one may or may not be appointed to you).  Recite the facts of your case to them fully and see what they advise as to your best course of action on the charge.  Experienced counsel may well be able to offer a defense to the charge and get it dismissed.  Had you been charged with an MIP, possibly not so.

Additionally, even if an attorney cannot get the charge thrown the good news is that you are 19.  This offense is normally considered to be a Class C misdemeanor but for a minor the punishment terms are the same as if you committed the offense of Possession of Alcohol by a Minor.  The maximum penalty for an MIP is usually around $500, a suspended license until you are 21, and community service depending on your past history and the opinion of the judge.  The judges may be more lenient depending on your specific situation.

Note:  Since money seems to be an is an issue, if you are not appointed a PD, see if you qualify for Legal Aid or see if they can recommend someone to help you.  Also, check if there is a law school nearby to where you live; they typically run free/low cost clinics that handle these type cases.  Finally, you contact the local Bar Association in your county; they may have a list of attorneys who will take your case "pro bono" (for free) or at least for a reduced fee based on your income/circumstances.