THis likely has nothing whatsoever with dry eyes. These are most likely floaters in the vitreous and since they are new you should see an ophthalmologist for a complete dilated exam to look for things like a vitreous detachement or vitreous hemorrhage or retinal detachment.
i experienced the same. you maybe lucky and not end up with an retinal detachment. i had your symptoms due to vitreous hemorrrage (spiders and dots) then it led to retinal detachment approx 3 months later. go see your eye doc to check you up and it will be most likely wait and see until you do or don;t end up with retinal detachment. if you are very near0sgihted you have higher chnace of getting retinal detachment. good luck.
These are not related to the dryness and may represent a posterior vitreous detachment. I would advise seeking the care of an eyeMD to make sure that you do not have any retinal issues, such as tears, holes, or detachment.
Sandy T. Feldman, M.D., M.S.
ClearView Eye and Laser Medical Center
San Diego, California