Hi. I will be happy to address your question. I assume from your description that you vision has not been affected.
The most common cause of a painless blood red area in the normally white part of the eye (conjuctivia and sclera) is a subconjunctival hemorrhage. This can be thought as a "bruise" on the eye. Unlike a bruise on you arm, which is blood under thick skin, a subconjuctival hemorrhage is blood under the tissue paper thin conjunctiva which covers the white part of your eye (sclera). Because the overlying conjuctivia is thin the affected area on your eye looks blood red, kinda like raw meat, instead of blue/purple like a regular bruise.
What causes this? Well, many things, such as being on too much blood thinning medicine, valsalva (coughing, sneezing, straining, etc), some types of bleeding disorders, hypertension or orbital mass etc. This being said, do not worry. The most common cause of subconjuctival hemorrhage? Nothing specific....and therefore nothing to worry about. It is not serious even though it looks really bad :o)
The blood can spread around the eye over a few days and then, like any other bruise, it starts to clear up, perhaps change color some and over the course of 3 or 4 weeks resolves without any treatment or residual damage. If you eye seems irritated you can use some artificial tears 3-4x/day.
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Both Methotrexate and Leflunomide help with your arthritis by immunosupression, albeit by different mechanisms. As such both of these medication have the potential to cause severe bone marrow suppression, liver damage as well as other organ damage.
Since these medications are being closely monitored by your rheumatologist, and you are having no other symptoms of toxicity I would not, based solely on a subconjuctival hemorrhage, worry about these drugs that you have been on safely for such a long period of time. It might be prudent, however, to mention to your rheumatologist that you had a small subconjuctival hemorrhage just to keep her informed. I do not believe these drugs contributed to your eye problem.
After about age 40 people start to need glasses to see up close. This is called presbyopia, it is normal and is nothing to worry about. Go to the dollar store and buy the inexpensive "cheaters". and put them alll over the house and car...that is what I do :o)
I hope this has helped.