I don't think making a new account just for your Teams access is very convenient. The desktop application is only associated with 1 account at a time.
So (until Dropbox changes something) there does not seem to be a good solution to your question.
So (until Dropbox changes something) there does not seem to be a good solution to your question.
It sounds like this was a summer internship, having to lug a separate computer around because Dropbox doesn't support separate accounts seems like a huge work around. The whole point of Dropbox is that the files are wherever you need them.
On the downside, the size of the shared directories would probably push the size limit of your account, so it's not a perfect solution.