First off I am sorry to hear that you are having problems with dizziness
in the morning, and when standing. There is no way for me to tell for sure what is going on without taking a thorough history and a good exam, so this forum can't replace a visit to your physicians office. However, I can give you some thoughts as to what might be going on. From the brief history that you have given, my first thought is that you may be experiencing something called orthostatic hypotension.
Essentially what this means is...when you are lying flat, your heart is not having to pump against gravity, so it doesn't pump quite as hard, and your blood vessels relax a little. When you stand up, all the sudden gravity starts to pull the blood towards your legs away from your heart and brain. Your brain is a selfish organ, so it tells your heart to pump harder, and your blood vessels to contract which helps increase the blood flow to your brain (there are pressure sensors that help determine this). As this process is taking place, occassionally your will get dizzy as a result of decreased blood flow to your brain. If the pressure sensors don't work fast enough, and your brain doesn't get enough blood flow, you can actually faint.
Then you will fall flat and gravity is no longer pulling the blood into your legs and you brains gets more blood and you wake up. This process can be exacerbated by dehydration, so make sure you are drinking plenty of water. Also you could try sitting up from lying for a few seconds prior to standing to give your body a chance to catch-up. If the dizziness persists despite these changes, I would recommended getting checked out by your physician. Best of luck. Hope this helps.