GH is released in pulses. So GH labs are sort of useless most of the time.
GH causes the liver to produce IGF-1 which has a longer half-life. So IGF-1 is a better lab for GH status than GH itself.
A thyroid problem with the pituitary would be low TSH and other low thyroid output hormones. If TSH is >=1.0, pituitary is probably fine in that regard. You also need to consider your iodine intake history [iodized salt] and body temperatures. See the thyroid basics sticky.
Hypogonadism and [subclinical] hypothyroidism are frequently seen together in this forum.
If GH is low, cortisol can be elevated.
If cortisol is high, GH may be low.
Prednisolone and other corticosteroids can depress GH or create a full GH deficiency during treatment.
Problems with 3 or more pituitary hormones has a name: pan-hypopituitarism
AM cortisol [do lab at 8AM]