Yes, it is possible for you to cause bloodshot eyes after gallbladder surgery because of the unstable eyes pressure and eye nerves. You'd better protect the eyes very much. You could use some home remedies to make your eyes feel comfortable and convenient. You could use the warm compress to make your eyes feel comfortable.
Well, in some degree, it can occur after the surgery, so you do not need to worry about it. Generally speaking, by doing the surgery, it can resolve some eye problems, but on the other hand, it may weaken your eyes during the recovery period. So your eyes will be sensitive, and then be easily infected by some irritants. At the time, your eyes will be red and bloodshot. So to treat it, you can just try some cold teabags under the eyes, and then it can be fine. Also, just try to protect your eyes after the surgery, or it can slow down the recovery process.
Usually gallbladder surgery won't cause bloodshot in eyes directly. Gallbladder surgery might leave patient with side effects like pain, diarrhea, breathing difficulty or bile duct injury. For the first week, the patient might experience serious discomfort and pain, because the internal organs are shifted or the carbon dioxide gas left in abdomen. Within 2-3 weeks after this surgery, patient might develop diarrhea due to frequent movement of bowel and bad digestion. As to bile duct injury, nearly 1 in 5 patients who took this surgery is affected. It is common as well as serious, which requires another surgery to fix. Yet there seems no clue between bloodshot in eyes and gallbladder surgery. There are too many causes of bloodshot eyes. You might get it for weight lifting, dryness of eyes, allergies and eye strain and so on. It is really a small problem, because the bloodshot usually clears out soon, even with no treatment. If you still feels bad, I suggest you do some saline solution compress on eyes, which might make you feel better, and give your eyes some time to have a rest, and also wash eyes out of irritants and lubricate eyes. Hope this could be helpful.