It sounds like you’re on Sublime Text 3 (the current version is “4”, though in reality it has no explicit version number any longer).
Starting in Sublime Text 4 the update dialog will tell you what build you’re running, what the new build is, and wether or not your license is still valid for it.
Since you’re using version 3, that part doesn’t apply. In that case the advice would be that if you have purchased your license within the last 3 years, it will be valid.
The worst case scenario for you here is that you upgrade to the latest build of ST4 by using the update dialog, and once the new version starts it may say “License upgrade required” in the title bar; it will still be fully functional though.
So in that regard, the most expedient thing might be to upgrade it and see what happens. If you need a license upgrade it will tell you, and you can proceed with that if you like what you see. If not you can re-download the previous version and set "update_check": false,"
in your preferences to turn off the update check.
Either way your current license remains valid in perpetuity for the last build to which it applies (presuming it doesn’t accidentally get leaked or similar, in which case you’d have to ask for a new one).