Here's a little basic stuff, perhaps less than you know already. I hope others will chip in with information I leave out, and correct anything that needs correcting (though I'm deliberately oversimplifying a little).
Your lymphatic system is a network of vessels and nodes (glands) that transports fluid and helps prevent infections. Your arterial system (arteries) transports oxygenated blood from your heart throughout your body. When it reaches its destination, it diffuses from the capillaries into cells and interstitial spaces, dropping off what needs to be supplied (oxygen, hormones, glucose, etc.) and picking up waste material to be transported away. About 90% of this fluid then returns through your veins, but about 10% is taken into the lymphatic system. The fluid that returns through the lymphatic system includes larger molecules of fat and protein, and in a normal system is filtered through your lymph nodes and then returns to the venous system. If for some reason your lymphatic system is not equal to the transport task, protein molecules accumulate in the interstitial spaces; they attract water, which leads to swelling, which is lymphedema. Early in the onset of lymphedema, this swelling can often be relieved by elevation, but over time the stagnant concentration of protein and water causes chronic inflammation, which leads to fibrosis (hardening) of the tissues, which further impedes the movement of fluid. At that point elevation will no longer get rid of the swelling.
The most common cause of lymphedema is surgical or traumatic disruption of the lymphatic system. In connection with cancer surgery, lymph nodes are often removed for examination to see if the cancer has spread to them, and thereafter the patient is at risk for lymphedema. That's called secondary lymphedema. Lymphedema that occurs without mechanical insult to the lymphatic system is called primary lymphedema. In primary lymphedema, the lymphatic system is not properly formed, or does not develop properly. Primary lymphedema can be inherited, and often runs in families, or it can occur with no family history, just because for some reason there was an impairment of lymph vessel or lymph node development.
Primary lymphedema can show up at birth, but more commonly it develops later. Similarly, secondary lymphedema can begin immediately after surgery, but is more likely to show up later (often much later). This is because our lymphatic system is designed with a lot of excess capacity; we're supposed to have much more than we need. In a defective system, the system has to "work overtime" and call on this reserve capacity more and more. The system struggles to keep up, but eventually the transport demands exceed the system's capacity, and the system breaks down.
Unless you had some kind of surgery or traumatic injury, it sounds as if you have primary lymphedema. Primary lymphedema occurs more often in women than in men, and more often in the legs than in the arms. There's no way of knowing right now whether your lymphedema may spread to other parts of your body. There is a test called lymphoscintigraphy, which sends radioactive material through your lymphatic system and photographs the flow, which might be able to tell you how your lymphatic system is functioning and whether other parts of your body are at risk, but it is somewhat controversial. Many people think there's no point in having the test if the diagnosis of lymphedema is clear without it.
The most effective treatment available for lymphedema is Comprehensive (or Complex) Decongestive Therapy (or Physiotherapy). The names differ a little--sometimes it's referred to as CDP or CDT or CLT, etc.--but the treatment is basically the same. The centerpiece of the treatment is MLD (manual lymph drainage), a gentle massage of the affected limb and the lymph channels from that limb to adjacent quadrants of the body. It's designed to move fluid out of the limb(s) into the areas where lymphatic circulation is better and can transport it into the venous system where it's supposed to end up. Each massage session lasts 50 minutes or so. It doesn't hurt; in fact, it's quite restful. Most commonly, two to four weeks of treatment are needed to reduce the swelling to as close to normal as possible. Most commonly there are two massages a day during this period (one in the morning and one in the afternoon), but some people get only one per day. In either case, you have to have your limb(s) wrapped in bulky bandages at the end of each massage, and keep it wrapped until the start of the next massage. (At first your therapist will do the wrapping, but gradually you will learn to do it.) That's to keep the fluid that has been drained out from flowing right back in again. At the end of the course of treatment, you will be advised from then on to wear a compression stocking at all times during the day, and to bandage the limb every night. Other elements of CDP include keeping the skin of the limb(s) clean and lubricated, and some light exercises you can do while bandaged.
Compression pumps are also used for the treatment of lymphedema, but there are problems with them that make them a less desirable alternative. There are people on the list who've had experience with pumps, both bad and good, and can give you more information about them should that form of therapy be proposed for you.
I suspect that the clinic your doctor has signed you up for is a CDP program. Normally, that would be good. The only thing that concerns me about it in your case is that you describe your legs as red and agonizingly painful. I would be concerned that you might have an infection (cellulitis, lymphangitis) in them, and if so, MLD would not be a good idea until the infection is treated and eliminated. Infections are very common in lymphedema, because the stagnant lymphatic fluid is rich in protein, and therefore a great medium for the growth of bacteria. An infection is often what precipitates lymphedema. Are your legs also hot? Itchy? Did you recently have a cut or other skin break in the leg that swelled up first? I think you should discuss the possibility of infection with your doctor, if it has not already been ruled out, before going to the clinic, or at least discuss it with the clinic personnel.
Hope this helps. Good luck to you.