Do glands only swell when you have a throat problem?

There are several structures in the neck that can swell, as you are describing. The most likely scenario is that you have enlarged lymph nodes, although it is also possible that you could be feeling enlarged salivary glands. In any event, there are many different things that can cause enlarged lymph nodes (or salivary glands), and you are correct in thinking that one of the most common things is a bacterial infection such as strep throat. However, even in the absence of symptoms of an upper respiratory bacterial infection in the sinuses, ears, mouth, or throat, it is still possible for an infection caused by a virus to lead to swollen lymph nodes (ranging from the common cold virus to more serious infections such as HIV). Other inflammatory diseases can cause swollen lymph nodes. In addition, cancers of blood cells (leukemia and lymphoma) can also present with swollen lymph nodes. The best thing to do as a patient is to see your primary care doctor right away. Swollen lymph nodes can represent a minor health issue that will go away without treatment, or they can be the presenting symptoms of something much more serious that should be addressed right away. Your doctor can take a thorough history and do a complete physical exam to help determine the next steps in diagnosing or treating any underlying issues.