I dont think there is a way off telling how long you have had trich for. It is a parasite that is usually passed on by having penetrative sex with someone who has it.
You can catch it without knowing for several weeks. It ususally affects women more than men as I have heard. I have once had vaginal trich a few years ago, and it was about a month before I got any symtoms, which was itching/soreness and discharge that was pale green/yellow. You can be tested for it at a gum clinic and it can be treated with a course of metronidazole. The person you think you have caught it from should also be tested and treated even if they dont have symtoms, otherwise if you had sex with them again, they could easily pass it back.
A STD test and medical personel CAN NOT tell you you've had such and such STD for such and such time. Only you would know when you had the potential exposure.
We cannot tell you how long you've had something, we don't know your sexual history and testing history.