TSH is a pituitary hormone produced to stimulate the thyroid into producing hormones. It should never be used, alone, to diagnose/treat hypothyroidism. That said, yours is high enough to indicate hypothyroidism. Combined with your symptoms, I'd say yes, you are hypo.
T4 and T3 are the actual thyroid hormones. The thyroid mostly produces T4, but also some T3, though the majority of T3 is converted in the liver, along with other organs, to a lesser degree. Some of the T4 in your system will be bound by proteins and will not be usable. That which is not bound by protein is "free" to be used. Same goes for the T3.
FT4 can not be used directly by the individual cells; it must be converted to FT3, which is the hormone that actually enters the cells; therefore, T4 is considered a "storage hormone".
Both levothyroxine and liothyronine are thyroid replacement hormones, but they don't do the same things, exactly. Levothyroxine is a T4 medication, and in a perfect world, the T4 would be converted to the usable T3, but not all of us convert properly, so we have to add a source, of T3, to the regimen to actually "eliminate" hypothyroidism.
We really need to know the actual levels of the T3 and T4, and whether or not they are for Free T3 (FT3) and Free T4 (FT4), or if the tests were for Total T3 (TT3) and Total T4 (TT4). Testing for totals is considered obsolete and of little value, but many doctors continue to test them anyway. Please post their results, along with reference ranges for each, since ranges vary lab to lab and must come from your own lab report. Please specify if they are Free or Total. If your lab report doesn't designate, they are total and of limited value.
All of that said, it's not unusual to see TSH above range, with normal, or low normal, FT levels. Hair loss is a symptom of hypothyroidism and It's also not unusual for symptoms to lag behind treatment, particularly, if your levels aren't coming up well.
It IS unusual for a doctor to jump you all the way from 5 mcg/day to 25 mcg/day, since 25 mcg/day is a pretty hefty dose of T3, and there may be a dose in between that will work well for you. Additionally, most people find that splitting their total T3 dose into multiple doses throughout the day, works better, since T3 is fast acting and peak within a few hours. It's not recommended that you take T3 medication after 3:00 pm, as it may interfere with sleep. T3 med has the potential to make you go hyper much more quickly than T4 med.
I can't tell you how to dose it, but you might talk to your doctor about starting out on a lower dose and work up - such as 5 mcg in the morning and 5 mcg around noon. You might try that for a few weeks, and retest, then increase a bit more if needed. Always best to increase slowly, with thyroid med, but especially with T3 med.
With the elevated prolactin and irregular menstrual cycle, I might suggest that you get tested for PCOS, which can sometimes accompany hypothyroidism.
Have you been tested for thyroid antibodies to determine if you have Hashimoto's Thyroiditis?
i should also add that since my thyroid symtoms stated taking place about 2 years ago, I have had a continuous stiff neck in which nothing seems to help it. Are they related? My dr's all say that it has nothing to do with the thyroid.