Welcome to the forum!
Intense pressure early in the morning while you are getting up can be due to severe acidity with probably duodenal ulcer. This is felt especially in the morning hours when the stomach is empty. This is the time when the effect of acidity is felt the most. The trick is to take a late night snack and keep some cracker at hand at the bedside. Also you would need to follow other lifestyle changes such as: avoid heavy meals and take frequent small ones. Avoid too much of caffeine, tea, 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. Go to bed at least 2 hours after food. You could talk to your doctor regarding a change in prescription or adding an antacid gel or something like Peptobismol.
The other possibility is pancreatitis. This can be detected by testing for pancreatic amylase and lipase enzymes in the blood and doing a CT scan. Liver function should also be tested.
I would strongly recommend you to see a gastroenterologist (a specialist who looks after the diseases of our digestive system). Please let me know if there is any thing else and do keep me posted. Take care!