Not a stupid question, but pretty much not at all. In fact, you are slightly immune compromised by the first pathogen against the second pathogen because your adaptive immune system is highly active against the first pathogen. The body has two systems, an innate immune system that has mechanisms to innately attack bacterial and viral pathogens in general and an adaptive immune system that adapts to each specific pathogen. The innate system is a first line of defense but is like a form of combined suicide bomber and cannon fodder throwing cell after cell to overwhelm the pathogen with death and there is significant collateral damage. The adaptive immune system takes time to ramp up to each new pathogen and if it's working on one pathogen doesn't really switch to working on the other. Rather older cells are/have adapted to the first pathogen and newly born cells begin to work on adapting a defense to the new pathogen. This takes time and there are, at the beginning, very few cells adapting to the new pathogen.