If I'm taking medications properly, how long will it take for hashimoto's thyroiditis to go away?

Hashimoto. Highly variable but response to treatment should definitely become apparent in 4-6 weeks.
It depends. It depends upon what you mean by "hashimoto's thyroiditis". Hypothyroid symptoms should clear up within 6-8 weeks of treatment with a dose that makes the TSH normal. Inflammatory symptoms (pain & swelling in the thyroid), get better in in most cases within a few months, but can persist for years in other cases.

Related Questions

How long can a chronic urticaria last? Apparentely it is related with hashimoto thyroiditis. Any idea? Its been 1year of hives and angioedemas.

Can be a long time. The association with hashimoto's thyroiditis is generally just thought to be that people who make antibodies to one thing inappropriately (thyroid) are more likely to make antibodies to other things inappropriately (mast cell receptors which can be a cause for urticaria). Most chronic urticarias last 2 weeks to 2 months, but 10-20% can last more than 2 years. Read more...

What weight supplement or fat burner can I take that's safe with hashimoto thyroiditis, eat healthy but still struggle losing the weight?

Exercise. Exercise regularly (both aerobic and strength) will help you burn off fat. Of course one must control the diet intake especially re to carb. If your thyroid replacement dose is appropriate, your weight gain has nothing to do with the thyroid. It is also not just how "healthy" but how much you ear compared to the energy expended. Read more...