At night, will get waken up in a "start", feeling of can't catch breathe, heart beats faster. Sometimes sweaty. Anxiety, panic, sleep apnea?

Chemical mattress? Dr. Fowler's advice about sleep study is good. Also I see you have a history of allergies. I have seen similar symptoms result from exposure to off-gassed chemicals from memory foam mattresses. If that's what you're sleeping on, try sleeping on the couch for a week to see if symptoms remit.
Sleep apnea. Although these symptoms are suspicious for sleep apnea - a sleep study would be needed to diagnose your problems. I would talk with your primary care doctor about a referral to a sleep specialist. Take care.