It's really going to depend on the specifics of your non-compete agreement. Not all non-competes are drafted equally, therefore, you should meet with an attorney and have them explain the dos, don'ts, and nuances to you.
These answers are not intended nor shall it be deemed to be the rendering of legal advise, they are given based on the information provided which is insufficient to give meaningful advise. These answers shall not be construed as part of the creation of an attorney-client relationship, nor shall it impose an obligation on the part of the attorney to respond to further inquiry. The Questioner has responsibility of obtaining legal advise from an attorney and is urged to do so.
What does your non-compete clause state? Is "everyone" who advised you attorneys? More than likely you are fine but we do not have the benefit of reviewing the language in your clause or the nature of your work so we cannot answer for sure. However, why are you asking IL lawyers about a NY contract when you intend to move to CA?
If you are in New York, contact an employment lawyer licensed in the state of New York. if you do not reside in New York, or your work is someplace other than New York, you should contact a local employment law attorney, who in turn should probably contact a New York lawyer (assuming that there is what is known as a forum selection clause).
Do it now! You do not want to make a move without knowing the potential consequences.
If you found this Answer to be helpful, please mark it as such. Remember, however, free advice is worth every penny you paid for it. This is only generalized commentary on your question. It is not to be taken as legal advice. I am a lawyer – but not your lawyer! Even "in person" interviews leave attorneys with plenty of questions – the Internet makes it crazy!
I would look to the agreement to see what state's laws will apply to the contract. Further, I would see if the agreement has forced you submit to New York's jurisdiction, should litigation arise. My concern would be that even if a matter is unenforcible in California, your former employer can sue you in New York and force you to answer to New York courts.
Please note that this answer is for informational purposes only and should not be construed as legal advice or an offer to form an attorney-client relationship. It is always advisable to seek the help of an attorney licensed in your state before proceeding on any legal matter. Good luck!