Alex I can sympathize with you very much as i am very similar to you! I have been a hypochondriac and struggling with health anxiety since i was 10 years old, and i have to say it is the hardest most awful thing i have ever experienced!
I can understand what you say about your family becoming annoyed with your worries over your health because my family find my obsessions over my health very hard to deal with. But just know that the only reason they are frustrated with it is because they want you to trust them that if they ever thought that there was something even slightly wrong with you they would have you at the doctors straight away! You must just trust them, but i know that is very hard to do too!
In regards to your worries over cancer i can sympathize here too. I have been convinced i have had every single type of cancer possible to the extent where i would believe is so much that i would get lots of worrisome symptoms (all in my head) and i would stay up all night shaking and crying convinced that i didn't have long to live. My Grandma passed away last month from cancer and the other year my boyfriend was diagnosed with a very rare form on cancer and this has only made my anxiety over having cancer and dying 100 times worse. But i know it is important for me to just try and remember that just because they had it doesn't mean i do, and that the only reason i feel like i do have it is because i am so worried over it.
Please also remember that the dizziness, lightheadedness, headaches are ALL very very common signs of anxiety and tension caused by your anxiety and are most definitely nothing to worry about. I certainly get dizzy and lightheaded very often. I can assure you that you don't have a brain tumor you merely have anxiety and a little bit of tension, all very common!
My advice to you would be this. Whenever something is bothering you and you think it is something serious tell your parents about it once, and it they aren't concerned the first time and second time leave it, trust them and don't bother about it again. Try try try to forget about it! Also, i don't know if you do this, but don't google any of your symptoms! This has had me convinced of so many things before and has definitely made my anxiety worse! Finally, try to remember more than anything that the reason you are convinced you are really ill is just because of your health anxiety and nothing more than that! Also remember that at your age, although it is possible, cancer is EXTREMELY rare (this includes you thinking you have a brain tumor)! Remember this when you get these thoughts.
If these things i have mentioned don't seem to work a good thing for you to do would be to go to the doctors like i did and tell them how much you worry over health issues. They referred me for CBT which i believe is suppose to be a wonderful way of overcoming health anxiety. They may also give you some medication to try and calm you down.
Please be patient Alex and hang in there! Remember your not alone and that there are many many people here to help you that are going through the same thing or have recovered
I wish you all the best!!