survivor0216,
Rupture of one of the blood vessels in the white of the eye is not uncommon after a bump to the head. These will heal on their own and do not need any treatment.
As to whether or not you need to see a physician, that is up to you. If you had a period of unconsciousness, even for a few seconds, then that would be classified as a concussion. If you went to the ER immediately after that, you would usually have a CT scan done, to rule out an epidural or subdural hematoma.
But, if it has been several days since you hit your head, you have had the “trial of life”. They would usually not do a CT scan now, unless you were having specific symptoms.
So, if you are concerned, you might want to contact your personal physician for advice on how to proceed.
Good luck.