@Asyn,
If you press a key "continuously", you get the same key repeated in almost any program or "field" you are working on.
The keyboard won't do this "by itself", and simple "dust" wouldn't do it either. But, just for example, some people tend to eat over their keyboards (and I have no indication that the OP is one of those). A piece of bread (for example) could have get into the keyboard and could be pressing some keys.
In (very) old keyboards, a simple piece of metal (commonly found in offices) could close the circuit and could give the same effect as if the user would be pressing a key.
Those are examples only, and I have no way to know if those examples are relevant in this particular case. I just though of a simple possibility, a different explanation, instead of thinking that a terrible malware is somehow controlling the system. By cleaning the keyboard upside down and pressing all the keys, some "chunk" of dirt may fall out and the problem could be solved.
This was / is simple speculation, and I just suggested it as a potential alternative solution to a potential different problem that could be showing the same final behaviour to the user. Only the feedback of the OP can tell us if this somehow solve the problem or not.