Does my kitten have allergies?

We adopted a Siamese mix kitten about a week ago that was born around 2 liters of kittens. In the past couple of days we have began to notice that he regularly gets little eye boogers throughout the day. I get the boogers out of his eyes every two hours or so and they continue to reappear through the day. After we noticed that, we started paying a bit more attention to him and he also seems to sneeze throughout the day. We are wondering if maybe he has allergies? We'll be able to take him to the vet in a week or so when cash flow is a bit more fluid, but we are concerned that if he has an infection it might spread to our other kitten, who seems super healthy and is about 14 weeks old. Our little Siamese boy is only 6-7 weeks old, if that has any importance as well. Any input would be a big help!