Bought second plan to be able to use apps on my 3rd comp

(someone more expert may wish to respond, but I believe this will help you.) Creative Cloud apps are allowed to work from a desktop computer and a laptop, as I understand it, but not three computers at the same time. This is so the owner of the plan can have the flexibility to work in the office and travel with a portable device and work on projects without copying assets back and forth between the computers. You would have to log out of your Teams plan on one of the first two computers to log into the Teams plan from the 3rd computer, and I don't believe you can be logged in under two different IDs at the same time on a single computer. Your "3rd computer" and the separate Photoshop and Lightroom on it are basically separate entities/individuals than your main Adobe Plan for Teams. You need to share assets and projects from the Teams plan with your "3rd computer" plan through Creative Cloud folders and libraries, the same way you would if you wanted an outside person to be able to collaborate on your projects. This could allow you to see what is happening with projects being worked on via the Teams plan while being logged in on your "3rd computer." -- Note: The ability to use the CC apps on a desktop and laptop is not intended for allowing two different people to be using the same login at the same time. -- You may be best served to contact customer support through your Teams plan so you can have a phone conversation or an online chat that is directly interactive and will help you get all your answers you need during one session.