Deep vein thrombosis (DVT) is commonly treated with blood-thinning drugs known as anticoagulants. The most common treatment is a course of anticoagulants, whether heparins, LMWHs, or warfarin. Anticoagulants are meant to prevent further growth of a clot or the formation of new ones while your body works to "dissolve" the clot more quickly. You will likely need to take the medicine for at least three months, and some people have to take them for life, depending on their risk factors and other health circumstances. However, in extreme cases, or cases where anticoagulants cannot be used, your doctor might treat your DVT with a blood filter installed in your abdomen. Compression stockings are also useful for minimizing swelling in the legs, and lifestyle changes like getting more exercise can help you manage your DVT.
Dizziness is a general, non-specific term often used to describe a variety of associated symptoms, such as feeling faint, lightheaded, nauseous, weak, or unsteady. If your dizziness is creating the sense that you or your surroundings are spinning, then that is more accurately called vertigo.  Dizziness is a common reason for doctor visits and is certainly uncomfortable and/or annoying to experience, but it's unlikely to represent a serious, life-threatening condition. There are many ways to overcome dizziness at home, but be aware of the "red flags" that signal the need for medical intervention.