A bad case of morning sickness (or in your case, all-day sickness) is not uncommon with twins, because you have higher levels of hormones circulating, which researchers suspect may be responsible for triggering your nausea.
Even if you feel terrible, the good news is that your babies are probably fine. If you were at a healthy weight and had a good diet before becoming pregnant, you likely have enough nutritional reserves to meet your babies' needs early in your pregnancy.
But you should still let your doctor know how you're feeling so he or she can monitor you more closely. The biggest risk is that you can become dehydrated, so focus on trying to get enough fluids. To tell if you're dehydrated, check your urine -- it should be a light yellow color. If you're peeing less than usual or your urine turns dark yellow, you may not be hydrated properly, and your doctor may want to put you on medications to help you feel better. In rare cases, morning sickness can be so severe that you may need to go to the hospital to recover, but this usually only happens if you've lost a significant amount of weight (meaning five percent or more of your body weight) or you become severely malnourished or dehydrated. This condition is known as hyperemesis gravidarum and there are resources available to help you if you think you have it. Don't let anyone tell you "it's all in your head."
Most women -- even those pregnant with twins -- start to feel better from morning sickness by the second trimester, so sit tight. You'll probably get your appetite back soon.