I had a transvaginal ultrasound and was told that if my tubes were blocked they would be inflammed and visible on the ultrasound otherwise they can't be seen. is that true?

Not necessarily: If there is active inflammation of the tubes they can be distended and visible on sono. Tubes can be obstructed and not dilated and not visible on sono. To diagnose obstruction an x-ray test -hysterosalpingogram involves injecting dye through a catheter inserted in the cervix and seeing if dye flows through the tubes. A similar test can be done with water and ultrasound to see if water passes.