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Since there is a tightness and since the problem aggravates on lying down, heart and lung causes have been ruled out, the symptoms could be exacerbation of the GERD. It could also be hiatal hernia. Treatment is a combination of drugs to reduce the acid and lifestyle changes. You will need to take a combination of medications (under medical supervision) like a proton pump inhibitor such as omeprazole, lansoprazole or pantoprazole empty stomach in the morning and an antacid gel after meals for complete relief.
Life style changes that will help include: Avoid heavy meals and eat frequent small meals. Avoid too much of caffeine, tea, smoking, fried food and drinks both alcoholic and non alcoholic fuzzy ones. Avoid heavy exercises within 4 hours of a heavy meal. Raise the head end of the bed by pillows to 30 degrees. Avoid lying down for least 2 hours after food. Maybe these tips will help you.
Since you have tachycardia, anemia, hyperthyroidism, low BP, and low blood sugar should be ruled out.
Since I cannot examine you and know other related conditions you may be having, nor is a detailed history possible on net, I have listed the various possibilities that should be looked into. Please consult your PCP for primary examination followed by proper referral.