I'm sorry you are still not feeling well.
I don't know a lot about Sheehan's, but it sounds like they did check your pituitary function by testing your pituitary hormone levels (PRL, GH, FSH, etc.). What do the docs think about the conflicting results and what the next step should be?
I don't know anyone personally who has Sheehan's but a search turned up an older thread on this topic. It's been a while but you could try emailing the original posters for info:
How low are your T3 and T4 levels (below range, 10% of range...)? Are they checking your free T3 levels (as opposed to total)?
Have they checked you for autoimmune thyroid disease by checking for anti-thyroid antibodies? (including Anti-TPO and anti-Tg and TSH receptor antibodies)
Are you taking any drugs regularly that could inhibit thyroid function?
Another test they could run is called reverse T3. High reverse T3 levels can cause low T3 levels, however rT3 is unlikely to be high unless someone is very sick.
Something your docs might consider is a TRH test to check your pituitary function. TRH stimulates the pituitary gland to produce TSH.
Sorry you are dealing with this, I hope this helps, or at least gives you some ideas to discuss with your doctors.