I believe Synthroid has a program for reduced pricing for those who qualify. Other brands do, too. Call a pharmacy and ask about their discount programs for Synthroid, or do to their website and see if they have one. Pretty sure they do.
I'm so sorry that this is possible with our current health care system in the US. You shouldn't have to worry about these things.
Thyroid hormone is made in the thyroid. Thyroid hormone is an essential hormone, and almost every cell on the body has a receptor for thyroid hormone. It regulates many different systems in the body. If you have no thyroid (I don't have one either), you have to take supplemental thyroid hormone, either T4 or T3. There is no "homeopathic" version that will help you unless it contains one of those two chemicals, at a dosage close to your current dose. If you don't take any thyroid hormone, over time you will experience worsening hypothyroidism symptoms, organ failure, and after several weeks to a couple months, it can be fatal.
If by homeopathic, you mean generic, then I can suggest trying levothyroxine, which is the generic form of Synthroid/T4. I take 137 mcg levothyroxine daily, and it runs me $12/month in Ohio. T4 is the inactive form of thyroid hormone, once it is absorbed, it gets converted to the active form of T3 throughout the body.
Other options for thyroid hormone include: natural desiccated thyroid - this is from pigs and is a "natural" form of thyroid hormone, as opposed to Synthroid or Cytomel which are both synthetic. (I don't know how much it costs, I've never tried it myself). Natural desiccated thyroid contains both T4 and T3.
I also take liothyronine/T3 (brand name is Cytomel), but that is more expensive than levothyroxine for me, at ~$20-30/month. My insurance has an extremely high deductible before medication is covered, so I check every month whether my insurance's discount or an online discount card is cheaper. If you have no insurance, you can go to a website like GoodRx and show a code to the pharmacy and receive drugs at a discounted price.
So... I don't know if homeopathic thyroid medication would be cheaper than generic levothyroxine, but if it does not contain the chemicals T4 or T3, it will not help you and will certainly not control your thyroid hormone levels.
Sometimes you can control the medication you need to take. If you have high blood pressure, you can possibly change your diet to lower it and get off medication. If you don't have a thyroid though, you must take supplemental thyroid hormone in some form, there is no other option.
To get generic synthroid, you need a prescription. If that is what you are most worried about (and completely understandable, the health system here does not work for all people), I think you have a few options. Some areas have free health clinics, or days where people without health insurance can get help. There are also low cost, online doctor visits that might work for you. (You would probably need a blood test, but that doesn't need to be done at a doctors office.)
I hope this helps. I'm so sorry you're in a position where you need to worry about this. Good luck.