I'm sorry you've had a traumatic experience.
I can only speculate, of course, without xrays of your current condition. But your description is quite helpful.
If you have numbness, I suspect there was some nerve damage. This can happen during an extraction procedure. And nerve damage can take months to heal. Generally, sensation gradually returns and numbness disappears. But it can be a long, frustrating experience. Sometimes steroids are used to promote healing.
Your TMJ symptoms are not surprising, given the trauma and length of the extraction process.An extraction can also change your "bite", or "occlusion". This can result in an imbalanced occlusion which may require adjustment to alleviate your TMJ symptoms. Stress can also contribute to TMJ. Your dentist might consider making a night guard to help ease your symptoms.
I'm not sure why you have the unpleasant taste. I suspect that once complete healing occurs, that too will resolve.
But I think it would be wise to see a dentist who is committed to addressing your extraction issue. Physicians are wonderful, essential health care providers. And your physician may prove more helpful than the follow up care you've received so far - I hope so. But physicians are generally not as knowledgeable about dental / oral issues such as yours.
Please let me know if you need additional information to answer your question. Otherwise I'd very much appreciate a positive rating for my effort. That is how I am paid for my work here.