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Just to clarify – you say that “Google told me I must start paying for Dropbox” … You may have gotten a message from Dropbox, but Google would not be the one sending that – Google does not own dropbox, they are independent.
Yes, you can use the Desktop uploader to grab photos from your Dropbox folder on your hard drive and upload them to Google Photos. Once you verify that they made it up to photos.google.com you can then delete them from your Dropbox folder and free up that space.