Theft in the Third Degree is defined as theft of property that does not exceed $750 in value. The crime is a gross misdemeanor punishable by up to 364 days in jail and a $5,000 fine. With no prior criminal history, and if you are well represented by an experienced attorney, you should not expect to serve any jail time. Further, depending on which court you will be charged in, your attorney should be able to negotiate some type of resolution that does not involve a conviction. A compromise of misdemeanor is also a possibility if the store is in agreement. The process will require several court appearances, and likely several months to resolve.
It is unclear exactly from your post whether you had actually left the store with the merchandise or if they actually discovered any merchandise inside your purse, but theft is a crime that must be intentionally, not accidentally committed. Unless the prosecutor can prove you intentionally deprived the store of the merchandise, it may be difficult to convict you.
Any theft charge is considered a crime of moral turpitude and a crime of dishonesty, which means it will have many long term consequences, including difficulty with employment or renting apartments, possible deportation if you are not a U.S. citizen, and being prevented from entering Canada. It is imperative you retain an experienced attorney to make sure you end up with the best possible resolution.
I think Mr. Nahajski's answer pretty much tells you everything you wanted to know. I just want to add a quick comment about the police officer asking you "the same question over & over," and the things you "admitted."
The officer was probably required to give you Miranda warnings before asking you these questions (I say "probably" because I'm not sure whether you were free to leave, but I'm guessing you were in a secure room). Almost everyone knows about Miranda warnings ("you have the right to remain silent..." etc.) because they are on TV. But, few people know how to exercise their right to remain silent. Usually being questioned by an officer is a high-pressure situation and people tend to feel that answering questions is the quickest way to escape the situation.
Unfortunately, answering questions does not help escape the situation, and is actually counterproductive. Often, a better strategy is to use the "broken-record technique." This is a technique taught in some schools to help kids deal with peer pressure. The person being pressured repeats the same statement (like a broken record) in response to increased pressure. For example, when offered cigarettes, the student can state "I don't smoke" in response to "c'mon, just try it," "all the cool kids are doing it."
When being questioned by the police, a good "broken-record" statement is "I want to speak to my attorney." It doesn't matter whether the officer is satisfied with your answer.
None of this is intended as legal advice. No attorney/client relationship has been formed.