I am sorry you are so young to be troubled with hypothyroidism. Make an appointment to see your GP and tell her you are not feeling good and could you please have another blood test. It is usual, when first diagnosed, to have a blood test every 4 to 6 weeks till you are stable. 25mcg is not a starting dose, it should be 50mcg (25mcg is an incremental dose thereafter) and 25mcg from then on until you feel well (although doctors only go by the TSH and not by how we feel (which should be the criteria). Also ask the GP for a Vitamin B12, Vitamin D, iron, ferritin and folate. We can be deficient and we need all our hormones/vitamins towards the top end of the ranges.
Get a blood test as early as possible and don't take levothyroxine before it, take it after. Get a print-out of your blood tests, with the ranges, from now on for your own records and to post here if you have a query.
We may also develop other clinical symptoms but unfortunately I doubt if a GP is aware of that. Sweats are common too as it is our metabolism which is affected by our thyroid hormones being too low. Weight gain is a common clinical symptom of hypothyroidism until we get to an optimum dose of medication.
We have to read and learn as much as possible ourselves if we want to get better. The thyroid gland hormones are a very important and drive everything in our body and T3 is the most important and our billions of receptor cells needs it in each a every one.
Levothyroxine, which is T4 only should convert to sufficient T3 but low doses are not sufficient, so we have to gradually increase till we have no clinical symptoms and feel well.
You take levothyroxine first thing with one glass of water and wait for around an hour before eating. If you take supplements or other medication, wait about 4 hours after taking levo so nothing interferes with the uptake of hormones.