If the "nephew" is feeling fine other than the snot, it's probably not a sinus infection. Yellow green snot is typical at the end of a cold. Is the nephew lethargic, have a headache, fever, ...? If not, I wouldn't assume it's a bacterial infection. My second had a cold for what seemed like her entire first year of her life and was always snotty. Sometimes it was clear and sometimes not. But there was no indication she had a sinus infection. When she had something other than a cold (e.g., an ear infection) there were other more obvious signs and we took her to the doc.
Excerpt from a medical site: "Clear, watery nasal discharge can herald the start of a cold. As the body begins to combat the illness, white blood cells rush to defend the injured tissues. This immune response turns the clear secretions cloudy and colors them green and yellow. It’s the natural progression of the illness, and the colors indicate only that the body is mounting an immune response."
That said, if your babies get sick every time you watch your nephew, then you have a good reason not to watch him. If it makes you feel better, the more your kids are sick now, the stronger their immune system will be and soon (probably within a year) they will be getting sick a lot less often. But, small babies being sick are the worst, so you might want to save that experience for later and just not watch your nephew.