Yes USPS expedited shipping does have a tracking number.
The tracking number for USPS expedited shipping is usually included with the shipping cost or at least it was the last time I shipped something through the service.
However if not you can request a tracking number but if you have to request a tracking number there will be an additional fee but it's not that much.
Still even when you have USPS expedited shipping there's no guarantee that the package will arrive any sooner than using standard shipping.
There have been times I've order something and paid the additional fee for expedited shipping and it took the same amount of time as standard shipping always did.
So in my opinion paying for USPS expedited shipping was not worth it.