Pattern recognition: a young mother with a history of massive postpartum haemorrhage who then cannot lactate, stops menstruating, gains weight, and feels tired is the textbook picture of Sheehan syndrome, that is, ischaemic necrosis of the anterior pituitary.
Reading the labs as a panel: LH is low and estradiol is low, so the gonadal axis is down (amenorrhea). TSH is low yet there is hypothyroidism, and TRH fails to push TSH up, so the thyroid axis fails at the pituitary level, that is secondary hypothyroidism. Prolactin is low and does not rise to TRH, matching the failure to breastfeed. ACTH is normal, telling you the corticotrophs were partly spared, a common feature.
Eliminating distractors: Hashimoto thyroiditis (option 1) raises TSH, the opposite of this case. Isolated gonadotropin deficiency (option 2) would touch only LH and FSH and cannot account for the low TSH, low prolactin, and flat TRH test. Primary amenorrhea (option 3) is impossible in a woman who has already given birth.
Several pituitary axes are knocked out together after a haemorrhagic delivery, so the answer is Sheehan syndrome. Ref: Williams Obstetrics.