Hi. I'm online and happy to answer your question today. I am an ophthalmologist
and would like to add a bit to what DrPauline has already stated.
There is no need to take him to a doctor. As DrPauline has already explained your father has experienced a subconjunctival hemorrhage. He does not have bells palsy and, in some cases, this can be extensive enough to cause his lid to pull away from his eye and cause puffiness. This should resolve.
In the vast majority of cases, sub conjunctival hemorrhage is nothing to worry about. It is usually not a sign of any serious condition but rather is just a small broken blood vessel in the conjunctiva that looks much worse than it really is.
No treatment is necessary. Think of a subconjunctival hemorrhage
as a bruise. The reason it looks so red (some people say it looks like a piece of raw meat) is that the skin on your eye is very thin so the underlying blood shows through easily. On your arm, for instance, a bruise looks blue/purple because the overlying skin is thick, blocking the red color of the blood.
Like a bruise elsewhere a subconjunctival hemorrhage will slowly go away over the course of a couple of weeks. It may spread around the globe some and change colors as it clears. This is nothing to be concerned about.
Since his eyelid is a bit distended it would be helpful to use some artificial tears to lubricate his eyes, not so much to decrease the redness (stay away from drops "for getting the red out" such a visine, as they will just irritate things....)but rather to keep his eye moist if needed.
Since he is on blood thinners, if he has not recently had his levels checked I would suggest he have this done in the near future just to make sure it is at a therapeutic level. This is not an emergency.
Your father can continue his usual activities, such as golf, although he will have to come up with a story of how the "other guy" looks to tell his buddies :-)
Does this make sense to you?
The nice thing about JustAnswer is that, unlike what you read on the internet, the information we give you comes from real doctors who are experts in the field. After 20 years of continuing ophthalmology practice I can assure you that your father will be fine even though his eye looks pretty scary!