It sounds like the software is reporting correctly based on what you just described. Removing software does not change the activation count. You must use the deactivation function provided in the software or have Adobe support perform a reset. At this stage the latter is what you need to do. YOu will need to contact Adobe support thru chat and have them perform the reset. You can try to get phone support as well, though they normally only support Cloud products lately - still you might get lucky.
For the link below click the Still Need Help? option in the blue area at the bottom and choose the chat option...
Serial number and activation chat support (non-CC)
http://helpx.adobe.com/x-productkb/global/service1.html
800-833-6687 (US daytime only 5AM-7PM PST, Monday-Friday).