The glands in the neck and the armpits, also known as lymph nodes, are a part of the body's immune system. As such, they do tend to swell periodically in response to infections. For example, when you get a cold or a sore throat, it is common for the glands in your neck to swell. However, after the infection trails off, they should settle back down. It would not be normal to have persistently swollen glands, especially in multiple regions of the body (for example, both the armpits and the neck).
One relatively uncommon but very serious cause of persistently swollen glands is lymphoma, which is a type of blood cancer. For this reason, whenever the glands are very large or persistently swollen, it is worthwhile going to see your doctor
to make sure that this is not a possibility. Other symptoms that would be concerning for a lymphoma, in addition to swollen glands, would include night sweats, fatigue, and weight loss
Your primary care doctor
can perform a complete physical examination. If they are at all worried they will likely want to get some basic blood work. Depending on what that shows, they might recommend additional tests as well.