If you did not sign a contract, it is non-enforcable. You never agreed.
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none.
Your employer cannot take your acknowledgement of receipt of one document as acceptance of a contract.
Before you make any employment decisions you should have the document reviewed by a local employment lawyer just to make sure it will not have an effect on your subsequent employment.
Typically, you need to sign a contract for it to be effective against you ... especially in non-compete agreements. It probably wouldn't hurt, though, to have an attorney review the documents. It sounds like additional facts (or wording in the handbook) could be important. It shouldn't cost that much.
The above statements are provided as general information and not intended as legal advice. Each matter has its own set of unique circumstances that cannot be adequately addressed without consultation. You are strongly advised to hire an attorney licensed to practice law in your state to represent you.
This is a tricky question. I am not a "Texas attorney" but have litigated many non-competes. The general rule of thumb is that a contract can be modified or created only when consideration is offered for the modification or contract. However, continued employment can, and often is, viewed as consideration. IN this instance when an "after the fact" non-compete is slipped in, if the continued employment was a condition it may be enforceable. You can have a non-compete invalidated for other reasons however, such as a lack of proper geographic limitation, or and overly broad scope.
The best advice I can offer in such a situation - if it is possible - is to go to your employer and ask them to give you a written waiver of the non-compete or to void that clause. If they won't you could also discuss with them some type of payment for any business you take, or solicit, that would be in violation of the non-compete. Good luck.
The following two issues are raised as to the enforceability of the contract: Consideration and Mutual Assent. Every contract requires Consideration and Mutual Assent. A non-compete agreement signed after employment has already begun may not contain proper consideration, as you were given nothing new or additional in consideration of your promise, and a mere promise is not enforceable. Additionally, every contract requires that both parties to the contract agree to it's terms. In this case, it doesn't sound like you had agreed to the terms of the non-compete, therefore it may not be enforceable. I would recommend having an attorney review the document for you prior to seeking competitive employment elsewhere. It would be a lot more affordable to hire an attorney now, than to wait until you get into trouble with your employer.