Should they just let me die ?

If the cancer was found early enough, it can be treated and possibly cured even to where you would live a normal life cancer free without remission.
Think of what you said/are saying, you're only 16 years old and have yet to know most of what you'll learn in life. Your doctor knows a great deal about cancer, especially if they're an oncologist, and took an oath to do no harm and only help patients that they encounter.
As someone who's been to the hospital so many times I honestly lost count, I know that being in the hospital sucks and treatments aren't always pleasant, but the feeling of freedom from illness and ailments after dealing with them for so long is unparalleled by anything short of love, actual love.
Listen to your doctor, don't listen to your doctor, it's completely your choice. Instead, listen to me right now in this moment. If you are threatening a doctor or anyone else with a gun and have the intention of killing them you may face a feat worse than death, incarceration in a small cell where you are only allowed to sleep and go to the bathroom and your meals are with hundreds of other people who are not afraid to be violent towards you... In my situation I had the option of giving up and letting myself die or sticking it out and seeing what the future would hold for me. Guess what, I stuck it out through brain surgery, countless tests and examinations, and even a brief time of technical death (I flat-lined once for under a minute). Now I am a college student planning to transfer to a university known to be good for my major soon, I have multiple jobs which I balance with school and homework, I can do things never thought of me before like driving and being more fit than ever before, and I can tell everyone that I survived 6 brain surgeries, an infection which should've killed me, and more "trauma" (I use quotation marks because it was more traumatic for people around me than myself) than most people my age, twice my age, or even 3 times my age.

Stupid hypothetical scenario showing you to be an ignorant troll

If you're somehow not trolling, I honestly think you should give chemo a chance because many people survive caner, but it really depends on your cancer.

Please try to avoid them if they are not real philosophers.

The doctor would either a) wait for you to fall unconscious and then treat you, or b) since you are threatening violence, sedate and then treat you. They probably couldn't do stuff like chemo, but they would do whatever they can to keep you alive.

Doctors have made an oath to always help those who are sick, and under no condition would they allow a minor to just die without trying to save him/her. If you were of age and terminally ill, then you could have a do not resuscitate order and possibly refuse treatment, but at 16 they will try to help you whether you want it or not.

The doctor does not however have the authority to bring you to a hospital for treatment, it's only after you're there that they can do that.

Not sure why you're so determined to die though. At 16 your body's repair mechanisms are at their peak and treatment would very likely be successful, depending on the cancer.

If I were the doctor and could reach cover, I'd shoot you myself, and then try to resuscitate you if I hadn't got myself shot in the process.
You're an adolescent twerp. The default position is that you don't know your own mind, and this kind of histrionics is evidence to back up that idea. If you made a rational and well thought out decision to die, that would be different, but it doesn't apply to your little scenario.

if you have a gun and want to die shoot yourself in the head with out taking anyone else's life. I don't see why the doctor can't only give you pain relief medication if thats your wishes? As your young and you only get one life why do you want to give up so easily. The doctor is trying to help you. Good luck what ever you do. Please don't kill anyone.

well then I just shoot the doctor and then shoot as many cops as I can before I get shot dead.
Because thats what would happen if they tried sedating me.

and by the time I fell unconscious from cancer, that would mean that I'm dead from it anyway.