Hi. I'm online and happy to answer your question today.
Sure. It is perfectly safe to pluck that eyelash. As a matter of fact it might help the stye to start draining if it is in the same spot.
Warm washcloths are just fine.....using tea bags really doesn't add anything (other then smelling good :)
Don't use the visine as it will just make things more irritated in the long run. If you can get some artificial tears (there are many brand names) you can use them as frequently as you like. They are available almost everywhere, including gas stations, nowadays.
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I think that the chat system in acting up as I noted you were typing but nothing showed up. I'll switch to Q&A and we can continue there....