A., I can't believe you just posted this because I'm having the same exact problem with my 1-year-old daughter with Down Syndrome. I have posted on some DS sites and most agree that it is the time of year, combined with the fact that DS children's tear ducts easily get clogged. I put a humidifier in her room last night and it was slightly better this morning. My daughter sees her pedi soon and I'm going to ask about it, but you might give yours a call and she what he/she says.
I doubt it is pink eye. Sophie's isn't.
BTW, I always love meeting other moms of children with Down Syndrome. Email me sometime if you want at ____@____.com.