Go to the doctor. You have a lot going on, but the chest pain with the sensations in your arm need to be addressed asap.
If it's not your heart, then could be gall bladder. I had a sick gall bladder that did not present as gall bladder pain. I had acid gurgling in my stomach, feeling full, stomach pain, a feeling of a rock in my gut, tired all the time, severe bloating in my gut. This went on for months and then one day concentrated on my gall bladder. I had it removed a few days later.
You should also look into the pancreas. My gall bladder surgery had complications and I had numerous pancreas attacks after surgery. The pain boars through the center of your chest and then radiates across your upper back. I also remember having two of these attacks several months before my gall bladder surgery.
Ultimately, I have gluten allergy which probably caused my gall bladder problems. If you rule everything out, then look into a food allergy.
If you are looking for a health professional's opinion, you might try the professional forum. As a lay person I can give you some ideas of what might cause some of this, but you it sounds like you need to see a professional doctor to me.
The first symptom one might guess constipation and a need for more fiber, such as daily metamucil, in your diet. Flatulence can come with stress, irritable bowel syndrome, constipation (I believe) and I don't know what all. Stomach pain can come with gastritis, ulcers, heartburn, cancer, and probably more. Lower abdominal pain can come from gas pockets, twisted bowel, constipation, endometriosis (if female), ulcerative colitis, appendicitis (if low right with rebound tenderness), and more.
Chestpain and strange sensation in shoulder to fingertips (if left sided)- you should make sure your heart is okay with a doctor. I've heard often females (if you are one) can experience a heart attack like heartburn. The may also check for a pinched/aggravated nerve about your shoulder, arm, and finger sensations, though you can have shoulder pain with a heart attack too. Esophageal spasms and chest muscle wall pain are a couple more examples of chest pain causes.
So bottomline, whatever it is, you have enough symptoms to warrant a trip to a well-trained doctor who really listens and isn't afraid to test you for things.