A.,
Bed rest hasn't been proven to stop labor, improve pregnancy outcomes or keep a woman from miscarrying if that's where the pregnancy is going. Bedrest in general is a bad idea for a pregnant woman. Your body, your uterus, your baby need oxygen, which won't be served by you being horizontal and immobile -- you need to move around, walk, get your blood moving. That does NOT mean do housework, vaccuum, move furniture, lift heavy grocery bags.... be sure to get all the help you need so you don't strain yourself.
The important thing is to find out why you are contracting so early. The things over which you have control are: nutrition, hydration, sleep, stress reduction, emotional peace. I hope you are getting the right nutrition in this pregnancy, and PLENTY of fresh water. Your caloric and nutritional needs are greater with twins. You need AT LEAST 100 grams of quality protein per day and I always recommend only 10 percent of that come from cow's milk sources of any kind (and go easy on fish). You should be eating a ton of fresh organic vegetables, lots of vitamin C-rich foods (kiwis!), eating some raw food daily, and taking a decent cal/mag supplement like the one by Apex. You should be eating every two hours. If you are not eating properly, start now. Reduce your stress and maintain a positive, calm home atmosphere. Eliminate toxins from your food and environment. Drink Pregnancy Tea or red raspberry leaf tea every day. Get a good chiropractor to adjust you. And pray.
As for whether you are actually in labor, there are no guaranteed predictors, but if you have "bloody show" (blood-tinged mucousy discharge), low persistent backache, and contractions that don't stop when you change something (lie down, walk, drink water, eat, etc.) and become harder, longer and closer together, you might be in labor. If not, you might be experiencing some wicked Braxton-Hicks contractions. See what happens when you change what you're doing when they come on to see if they stop or slow down.
As for the advice you're getting that "twins usually come early," you should know that this is NOT normal -- twins tend to come early in this country due to insufficient nutrition and doctor intervention more than anything. I have a good friend who is also a birth doula and childbirth educator who gave birth to twins, one a footling breach, at home unattended and they were both around 8 lbs and she did it all on a vegan diet, blowing a hole in about four myths about twins. However, if you lie around on your back, get no exercise, eat poorly, consume sugar subsitutes, radically reduce salt, fail to hydrate properly or get enough quality protein, and allow the doctors to perform any of a number of interventions, you are likely going to have a very hard time. But you'll be in good company, as this is becoming the common pregnancy experience in this country.
You should know, I'm not a "listen to your doctor" kind of gal when it comes to pregnancy. You might want to get the advice of a qualified midwife, preferably one with home-birth experience as opposed to a "med-wife." Be careful about that "shot" the doc might give you -- it's probably Terbutaline, which is an asthma medication and not approved for use in pregnancy. It might stop the contractions, but it can also cause heart complications in the babies and problems for you. I would try just about anything else first.
In the end, you have to do what you believe is right to give your babies their best chance. But it's your responsibility to educate yourself and do all that is in your power. The rest is up to God, and no, He's not the one in the white coat.