How long have you been on the increased dosage?
It's not unusual for one to feel worse before feeling better, once placed on thyroid hormones, as the body gets used to having the hormones it's been doing without. Additionally, when the thyroid is not producing enough hormones, the adrenals tend to try to pick up the slack, so when you start adding the thyroid hormones, the body has to readjust.
Also, it's very possible that you haven't reached the optimal dosage yet, to alleviate your symptoms, since it's customary to start out on a low dosage and work up as needed at approximately 6 week intervals.
Along with TSH, your doctor should be testing Free T3 and Free T4, which are the actual thyroid hormones and are much more telling than TSH. If you have results for either/both of those, please post them. Be sure to include reference ranges, since those vary from lab to lab and have to come from your own report.
Has a cause for your hypothyroidism been determined? The most common cause of hypothyroidism is Hashimoto's. Hashimoto's is progressive in that it is constantly destroying thyroid tissue until eventually, the thyroid is destroyed and produces, nothing. If you have Hashimoto's, you will need periodic adjustments in your medication.
To determine if you have Hashimoto's, you will need 2 antibody tests... those are Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb). You need them both, because some of us have one or the other and some of us have them both.
Well, of course, you have to be diligent in taking your medication or you will not get better, as the medication must build in your system and it can't do so, unless you take it consistently - that means on a daily basis, at approximately the same time every day. According to the instructions on the medication, you should take it on an empty stomach, with a cup of water and do not eat or drink anything else within 30-60 minutes of taking the medication. Food and drinks can inhibit the absorption of the medication, which can render it absolutely useless, which case, you will "not" get better...
Many doctors don't find it necessary to find the cause of hypothyroidism, because they "assume" it to be Hashimoto's. And yes, your student health insurance will limit you to the most basic testing and treatment.
It would be helpful to know the other tests that were done, as well as the results and reference ranges. You should try to get these each time they're done, so you can keep them for your records... That way you will know at which levels you feel best, since TSH is affected by many variables and can fluctuate by as much as 75% over the course, of a day. It should not be the sole determinant of medication dosage.