Can I get some compensation because I quit my job without notice?

It's possible, if you were a victim of discrimination based on age, race, sex, national origin, religion or disability.

I sue for employees all the time. If you're FORCED out it's called "constructive termination" and you'd have a suit possible.

You may be entitled to unemployment benefits. As far as other compensation, it would be difficult unless you could prove the stress of the job caused you injury, then maybe a worker's compensation claim could be brought.

Likely no. This is the GA DOL rule on unemployment comp: There must be some clear connection between the health problem and the performance of the job, and professional medical advice is required unless the reason would be obvious that harm to the employee would result from continued employment. This includes such obvious things as broken limbs, violent reactions such as allergies due to the environment on the job and similar circumstances. Provided, however, the employee must discuss the matter with the employer to seek a solution by another assignment or other changes that would be appropriate to relieve the medical problem before the employee can show good work-connected cause for quitting. Did you go to a Doctor? Did he/she tell you you needed job changes Did you tell the employer about the doctor, and ask for accommodations Did the employer refuse to accomodate? If you answered yes to all of the above questions, perhaps you can win. Otherwise, no.

Go ahead and apply for unemployment. It is difficult to get if you quit your job, but maybe you can show that the circumstances warranted it. If stress is truly the cause, then maybe you can get a doctor's note stating that continuing in the job would have been bad for your health.