you don't need to sign-out on any computer unless and until you start the sign-in on a 3rd computer. (and you will be prompted on that 3rd computer to select one fo the other two where you are still signed-in.)
and you will lose no work IF you've saved any in-progress adobe files. ie, if you open photoshop and make some edits on something and fail to save, yes - you will lose those edits.
otoh, if you save that file, you will lose nothing.
in the future, to find the best place to post your message, use the list here, https://community.adobe.com/
p.s. i don't think the adobe website, and forums in particular, are easy to navigate, so don't spend a lot of time searching that forum list. do your best and we'll move the post if it helps you get responses.
<moved from using the community>
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