There may be a delay in crediting the refund. That's normal. However, you should look up your original flight ticket and see if it's still in the system.

I would contact United Customer Service again and provide them with the information you got from the first 2 representatives you talked to. Since you already have other travel plans in mind, it may be easier and cheaper to make a change to the prior reservation rather than cancelling it for a refund (or no-refund!). You can even change origin and destination!