Is it possible to get second master while I already have one?
Your own health is more important than any degree. You should attend to that. If you can do both, perhaps working with a therapist while deemphasizing your degree work for a while, then that might be an option. Stress and depression are very serious. 

Your advisor seems to be invested in you, so you may have an option of a pause or a slower rate of progress. But a second masters won't impede your current goals so it doesn't sound (from here - which is far away) as a poor option. 

However, if you can find a therapist who can help you with the health issues, he or she would be a better source of advice on your future plans than anything you will get here. In fact you may get advice of a complete different sort that neither you, your advisor, nor the community here could think of. 

But for the direct question, I can't think of any downside to having more than one master's degree.