Why do I keep having eye hemorrhage in both eyes 10 years after Lasik surgery? What can I do about this?

Conjunctival hemorrhage at this remote date are not the result of your Laser Vision Correction. Such hemorrhages can issue from minor ocular trauma or from eye rubbing. If you are taking aspirin, Advil or preparations containing these drugs you might be more susceptible to sub conjunctival hemorrhages. 

Subconjunctival hemorrhages, or bleeding
in the whites of the eyes, can occur with violent coughing episodes, straining,
and severe eye rubbing.
Additionally, there are many medications which can “thin” the blood and
contribute to these hemorrhages.
Aspirin, non-steroidal anti-inflammatory medicines, and any
over-the-counter medications which contain these substances (Pepto-Bismol and
Alka-Seltzer, for example, both of which contain aspirin) can thin the blood.

Your LASIK surgery is not contributing to
you having these hemorrhages.
Assuming you do not have any underlying blood clotting disorder, they
are harmless and simply a cosmetic nuisance.