Why would they do epidural between c7 & t1 when the herniated disc is between c3 &c4 & c4&c5?

Symptom dependent: The location of epidural blocks should correspond to the area of referred pain. It is certainly plausible that the treating physician did not feel that the C3 disc was the cause of your symptoms and in fact the area in C7 region was in fact more likely to be causing your pain.

Anatomy: There are 2 different types of epidural injections in the cervical spine: transforaminal and inter laminar. Inter laminar injections are given near the midline of the neck They are typically given either at c6-7 or c7-T1 because there is much more space for the cord at that level and the injection will typically spread up to the other levels like C3-5. More danger to do interlaminar at c3-5.