You can buy the latest PSE 15 from Picture editor software, photo enhancement tools | Adobe Photoshop Elements 15 as per your required OS.
To continue working with this same catalog on newer version, refer to procedure mentioned here:
Move Elements Organizer catalog | Elements 6 or later . Please make sure to go through whole article before backing up and restoring your catalog.
Hope this is helpful. Get back to us in case you face any issues.
You may find that the price of the full version is cheaper than an upgrade through black Friday (November 25). If you buy the boxed version from on-line sellers you get disks for both windows and Mac. You can still install from an Adobe download and simply validate with the serial number from inside the box.
You should be able to do a full backup from within your iMac PSE 10, and then use the Restore command on your Windows PC. Assuming that you are backing up to an external drive, make sure that the drive is formatted such that it can be read by both computers. Once you have completed the restore process, make sure all of your tags etc are present.
You may find this video helpful. There are other posts in this blog discussing the backup and restore process for PSE.