Shaking is fairly common and usually happens after waking, google to see, there is a lot of it around ..,blinking seems normal also maybe good to ask the Doctor about it ..
Im wondering if he may have childhood diabetes
daycare said he drank water all day too
shaking/blinking isnt like diabetes.. yes thirst can be, it may be a good idea to ask for tests.How long is he in day care he may be missing you , what do they do in day care have they a good routine with the children .?.
The eye blinking may be a transient tic and it will probably go way , again best to ask the doctor ..