There is no possibility of Chia seeds causing cold sores. In fact, the opposite is true as Chia seeds enhance the immune system making infections of any sort more unlikely. Cold sores (Herpes Labialis) is caused by the Herpes Simplex Virus and once infected you are subject to repeated outbreaks.
Yes, I have heard that taking Chia seeds can cause some people cold sores and other crappy side effects. Chia really has no nutritional value, and you're better off eating other seeds or brown rice that at least has a nutritional value, that is just my opinion. To address the cold sores, start taking Lysine on a daily basis and that will help prevent them from flaring up. You can find lysine in the vitamin section of any store. Take care.