Nineteen-Year-Old Charged with Shoplifting

My question involves criminal law for the state of: Texas

I'm 19 and got caught shoplifting at a department store today (under $150) and was brought to a room and signed 2 papers acknowledging that what they found was all I stole and another paper that they said would mean the store would "sue" me. They called the police but they were not able to come within 2 hours so they let me go and told me that in a week I should call the police department and check for a warrant for my arrest. Once I find out there is one then I should go turn myself in.

My questions are:
1. Is there a chance that I'll be lucky and the warrant will not even appear?
2. If so, will I still be receiving a letter demanding me to pay a certain amount?
3. If I get that letter, should I just pay it since I already confessed to shoplifting by signing those papers?
4. Also, is there a way I can check for the warrant for my arrest?

1. There's a chance, but I wouldn't bet on it.
2. The civil demand is entirely independent from the criminal proceedings. If the store is the type to send such demands (and it appears since you signed an acknowledgement to such that they are), you can GUARANTEE you will receive such. The "lawyers" that send these letters live for the collection of these funds. They don't give a hoot if you get arrested or not, they just want the revenue.
3. That's up to you. You could end up being sued in civil court and there seems to be a preponderance of evidence against you. Many attorneys will recommend you do not pay the demand and call their bluff. The downside is that if they do sue you, the amount you'll end up paying will certainly be more.
4. You can call the police, but almost certainly the best way is to check your mailbox. Despite what you learned from watching TV, criminal proceedings aren't always started by arresting someone and hauling them down to the station. You may get your charges in the form of a summons in the mail.