Without knowing what your agreement holds, it is impossible for me to tell you whether you can quit working for the CA employer and go to work directly for the school. And that is your primary question.
Were you in CA, or if your agreement states that in the event of litigation that the laws of CA will apply---then I would tell you that CA makes it illegal for an employer to have a non-compete clause in their contract. But that is only a certainty where there is a CA employer and a CA employee.
I am happy to answer any question that you might have---but if you don't have the facts that will determine the outcome of the case, all I can do is tell you what the law states and when you know the facts, you will have your answer.
If you are sued in Texas, under Texas law, there would perhaps be a different result:
Like many other states, Texas law recognizes an employer's right to protect legitimate interests of their business, but the law also considers the need for an employee to earn a living. While the restrictions in a non-compete agreement may be enforced in certain circumstances, they must be found to be both reasonable in their duration, and in their geographic scope.
While a 5 year nationwide ban on competing would not be enforceable, a 1 year limitation within a number of surrounding counties in your area may well be enforceable.
Many such agreements are simply too restrictive and will not be enforced by a court. The only way to know for sure is to have your particular agreement reviewed by a local employment law attorney who can look at your present job---the overall business of your present employer, the nature of the competition in your locality and the restrictions the employer is trying to place on you.
Feel free to ask any additional questions that you have. In the meantime, because you can come back to this thread at any time---even years from now to ask a follow up question, I would ask that please remember to rate my service to you when our communication is completed.