Oh dear, at the risk of being really boring, no, I don’t think that I ever had a parasite myself, not that I know of. I may have had pinworms in my early childhood but my parents never told me about this.
I may have a parasite that is called Toxoplasma gondii, transmitted by cats, because I grew up with lots of cats (and dogs). I may also have a bacterium called Helicobacter pylori in my stomach, as every second person has them but these are not normally considered parasites.
So my boring answer is no, probably not, but if I did, I would probably put them in a jar or something like that and keep them on my desk all day long, with a sense of pride and ownership – these were MY parasites!