You don't have a copy of your employment contract?
Can you not just ask for a copy of your employment contract? For sure it might raise someone's eyebrow and they might suspect that you are being headhunted, but that's something that your employer should expect to happen as a normal course of business.
But as someone said above, most non-compete clauses are unenforceable in terms of just working for the competition. If there are no clients or staff or intellectual property that could be taken with you, then it's pretty unlikely that a restrictive clause would hold up or that the company would waste their resources taking you to court over just getting a new job.
If you opened a competing business across the street? That's a whole other matter, and usually they can reasonable demand that you give them a few miles of radius. That's really about it.
Mostly this, except the details vary a lot from state to state. Decent chance that if any non-compete was well worded that it passed through with your employment to affiliates, successor companies, subsidiaries and the like. Whether or not it’s worth it for the company to enforce would depend a lot on your role, where the competitor work is located compared to your current work, and politics (eg are you leaving the company in a huge bind by leaving at a critical point, or did you offer to work out notice and be cooperative if they desired it).
Also, you might not have an employment contract. For my company, there are no employment contracts. Your offer letter would contain stuff like starting title, pay, etc, but confidentiality, non-solicitation, and non-compete agreements are all in a separate document that if you asked for a copy of your offer letter, you certainly wouldn’t get sent automatically.
Disclaimer - Not a lawyer but have dealt with this from the HR of departing company side a few times.