Which kind of non-invasive test should i do if i wanna know whether my tube is blocked or not? can a mri or ct scan give an accurate answer ?

None: The only reliable test for this is a hystrosalpingogram

1st have a Sonogram: Endovaginal Sonogram is the best initial evaluation for infertility. It is relatively non invasive as it doesn't penetrate through the skin or mucous membrane. Hysterosalpinography can be performed with Sono or X-ray. I think X-ray is best after doing over 1000 of them.