Toddler nursing is seen as kind of weird these days, and though you wouldn't actually be nursing, but pumping and offering it in a cup, it kind of goes along with the territory. But the truth is that many children the age of your older so are still nursing and not only is it okay, it's actually quite healthy. But many people don't see it this way. I know I for one started out saying something ignorant like, "Once the baby has teeth, I'm cutting her off!" But here I am, nursing a 15-month old, with no intention to stop... and quite the advocate for such a practice, too. I think that when you have your own children, you realize that even though your baby is growing up, s/he is still your BABY. It makes a huge difference in how you feel about things like extended nursing.
And yes, I think that offering breastmilk instead of cow's milk when your son is stuffed up makes a lot of sense. Does he just have a cold? Or does he have allergies? Either way, your milk (and thus, your antibodies) will help make a positive change.