Valspar is a good quality paint. They make two grades of interior paint - the standard with low VOCs and the Ultra with no VOCs.
I'm not sure which one you used though even the standard low VOC grade should not cause an issue unless you are quite chemically sensitive; something you would likely know already.
I have a couple of questions:
- Who applied the paint? If it was you and you weren't immediately affected, then it can't really be the paint.
- Even if you had a painter apply the paint, I will hazard a guess that you would have been quickly affected as soon as you first walked into the room.
- If the room was painted before you put the furniture in did you notice your eyes burning then or after the furniture install?
- Did you change anything else at the same time? New carpet and pads are often high VOCs at first. Even having carpets cleaned can cause a VOC issue, depending on what the cleaner uses.
- Did you change anything else in your home - a new furnace, duct cleaning, new pet, anything else?
- Lastly, if you can't place the problem on anything else, I would suspect the furniture; they have lower environmental regulations in China so you can't really know what finish they applied.
My suggestion is to turn off the heat in that room, put a fan in the window blowing out, and leave it on low for a week to really ventilate that room. If it eases the problem, you can try installing the furniture again one piece at a time.
If there's still a problem with your eyes burning, even before you bring the furniture back in, you're going to have to call in an expert in indoor air quality testing to figure out what's going on.