Bad chest cough for about 3 weeks now. i've had a really hard time sleeping & mon. i started to feel pain in my mouth. white circle, touched and peeld?

Chronic cough: It could be a simple viral infection that has a residual ongoing cough or its possible that its now developing into a bacterial infection. Possible mouth ulcers. You need to visit your doctor who can examine your chest and mouth to see if you need antibiotics at this stage. You can also try simple home remedies such as steam inhalation or ginger and honey mixtures to soothe the throat irritation.

Last forever: This sounds like a post-viral cough which can last for weeks and there isn't anything that helps, at least that I can find. You just have to ride it out most of the time. As for the white circle in your mouth, it sounds like an aphthous ulcer, but difficult to say without seeing it.