The area under my left eye is red, swollen and tender to touch. I do not believe it is a sty or pink eye - what could this be?

Inflamed skin. If skin is red, swollen and tender to touch it is inflamed. The most concerning cause of inflammation is infection, so keep an eye out. Chronic irritation from rubbing or watering eyes can do it. Bug bites can do it. Sometimes allergies can do it, although these usually itch more than hurt until they get infected. You might also be in the early stage of a stye. Keep an eye out for a bump on eyelid.
Depends on where. As you suggested, chalazions or styes, are a common cause of inflammation of the eyelid. Other less common causes include a tear duct infection (dacryocystitis-usually below inner eye lid) or a cellulitis (infection of the skin). Both of these issues require topical and/or oral antibiotics and should be evaluated by an ophthalmologist. Of course there are other possible but more rare causes.

Related Questions

My eye when I wake up in the morning has yellow crust on my upper eyelid and the side of my left eye is red and sore I thought it was pink eye and I asked my school nurse and she said it wasn't help me please thank you

There . There is probably no way for the nurse to be sure of the diagnosis. This could be anything from an allergic conjunctivitis to something bacterial. If not better in the next 24 hours, i would see an ophthalmologist for diagnosis and treatment. Read more...
There . There are many problems that can cause your symptoms, as the other docs mentioned. Allergy is a little less likely, because it usually affects both eyes at the same time. For temporary relief, use some over-the-counter tear drops, or a 'get-the-red-out' drop for one or 2 days. If your vision is blurry, or if you have pain or increasing swelling, you should see medical care immediately. Read more...
Crusting . Crusting is a sign that your eye is trying to heal. It can be from an infection, debris or allergan in the eye. It is not possible to diagnose without a slit lamp (microscope used by an eye doctor). If it continues, you should be evaluated by an ophthalmologist. Read more...

I've woken up with a swollen and sore red eye. As far as I'm aware, it's a stye. Any home remedies to fix it?

Warm compresses. A stye is a swelling of one of the small oil glands on the edge of your eyelids. A stye causes redness, swelling and tenderness of the lid margin. The best initial treatment is warm compresse to to the lid margin for about 5 minutes 4 times per day. Read more...