please have a first look there, where you will find general infos about your Adobe Account
If necessary for more help, please use Contact Customer Care
It was not purchased under my adobe account, so I don't have access to that information. I also don't know the method of purchase. Customer care just loops me back to this. I can't just find the serial number on my computer?
if you don't get the necessary informations about the former account, it might prove difficult to use Transfer an Adobe product license but you should try it.
On the other hand I recommend to use contact by: "Telephone numbers of customer service and technical support Adobe worldwide"
>>> https://www.adobe.com/eeurope/elicensing/licensemanagement/alm/contact.html (I used Europe's link, but that makes no difference.)
I'm not clear why you are looking for YOUR serial to reinstall your CO-WORKER'S Acrobat. Were you sharing a single copy?