Wow. Tough situation. I have had a few jobs make me so physically ill that my muscles and joints hurt so bad and it became impossible for me to get out of bed. It was actually physical. I wasn't the main support for the family but for myself. The situation wasn't as stressful as yours since you support a family. I did get medicinal assistance, which did help.
You sound like a very loyal person and you don't want to let down your employer. That thought could also be adding to your anxiety and making you sick. I would still put out feelers for different job and perhaps even apply for them. If you do get offered a job, then you may have to think about this....are you more loyal to your job that is making you sick or to your family?? If you remain at this job, sickness may continue to rear its ugly head in your professional and personal life thus negatively impacting your entire life. Please don't do that to your family.
My husband and you sound very much alike. He is so loyal that he would be willing to stay sick and be completely stressed out because of his loyality to a job rather than quit. He finally had to consider the whole picture. He explained everything to his boss and his boss was completely understanding as he also has a family. It turned out so much better than we could have even imagined!
Have you had the job for a while or is it relatively new. If it is new, perhaps you just need some more time to get adjusted. That was my situation at the job that made me sick.