Shivangi1... it takes 4-6 weeks for the medication to reach full potential in your blood, so having only taken it for 4 days is not long enough for it to do any good. In addition, it's not unusual for symptoms to get worse before they get better and as I noted, 25 mcg is a very small dosage, so it will probably not be your final dosage.
Iron deficiency also contributes to hair loss, so once you build your iron stores, that may help.
The thing to remember is that it will take time for your body to recover from this illness. Try not to run your hands through your hair a lot and be very gentle with it, even when you shampoo it. The heat from hair dryers, curling irons along with styling products, daily washing, etc can be very hard on hair and may contribute to dryness and hair loss. You could try using baby shampoos and conditioners that are more gentle and see if that helps.
I agree with Barb. B12 should be at least 700 if not close to the very top. But anything less than 700 you will probably be fatigued with low B12 alone, let alone the lower thyroid levels you have.
T4 medication like you are on takes about 6 weeks to stabilize but 4 weeks is minimum before re-testing to see how the starter dose had any effect.
Be aware that your FT4 level could go DOWN, and often times people will feel worse after starting thyroid meds. This is due to your body reacting to the added medication and it takes time for the body to get used to the added T4. The levels can go down because your body sensed the added T4 and actually reduced your T4 thyroid gland production with a corresponding reduction in TSH. So you may end up with LESS net FT4 and feeling worse.
If that happens, do NOT let the Dr. remove the medication since your TSH is now magically in the so called "normal range".
What is important is to feel well, not obtain certain specific lab values. if you feel terrible it really doesn't matter if you are in the range or not.
It's customary to start with the T4 and if needed, add T3 later if you find you don't have adequate conversion to T3 in the body. It should be noted that 25 mcg is, typically, only a starting dose and will most likely have to be increased after the month is up.
Did your doctor recommend supplementing with Vitamin B-12, since your level is at the bottom of the range? This, too, will cause symptoms similar to those of hypothyroidism, as will the low Vitamin D level and the low iron/ferritin. You should be supplementing with both of those, as well.