Welcome to the forum! Yes, it's real hard to find good information on the net about birds, isn't it? It takes a lot of time, a lot of effort and a lot of knowing exactly how to phrase the question on the search engine as well as using different ways of saying the same thing - but you are in luck because you found us!
In reply to your question, yes, there are diseases, called zoonotic, that can be passed from animals to humans and viceversa. Thankfully for us and our birds, the common cold and the flu are not. Cold and flu viruses are actually very specific to the species they attack so a dog cannot catch a cat's cold, our cold or a bird's cold. And birds cannot catch our cold or flu viruses BUT we can catch psittacosis (the real name of the disease is actually chlamydiosis) from them and they can catch it from us. And psittacosis starts with exactly the same symptoms as a normal cold - only it goes into the lungs and gets much worse -all the way into severe pneumonia- requiring a long treatment to cure it.
So don't worry about it, even if you had touched your bird with hands that had the virus on them, he/she would not have caught it.