I can imply you bought your license in a box (with CD).
But I can't imply what version you have, nor whether you're using Mac or PC.
There are downloads for virtually all versions online, so as long as you have a good internet connection you should be able to download an installer, then use your serial number or Adobe ID (depending on version) to activate the software.
You may also want to deactivate the copy you have on the old computer when you have the new system set up.
-Noel