If you're in the US, a gynecologist is not considered a specialist. However, I use my regular doctor as my gynecologist. It's easier for me to get everything taken care of in one office. If you're comfortable enough with your GP, they should be able to take care of your basic womanly medical needs.
You should be able to call your doctor's office and speak to his/her nurse to see if this is something they can do for you if you're still unsure. (Sometimes you'll have to leave a message and they'll get back to you - they're usually busy!) You can explain to them that you're having an issue with a unpleasant smell, and that you're also worried about your period. This phone call should be confidential and might be a good opportunity to relay some of your concerns about your parent's lack of concerns, so your doctor can be aware handle your situation a little more appropriately.
I saw above that you're quite thin. I weighed about as much as you do when I was your age too. And since you've gotten your period, you're already ahead of me at that age! But honestly, I don't think that your missing period is a huge deal, but it isn't a bad idea to run it by a doctor to make sure there are no other underlying issues.
As others have stated, it sounds like a reaction to your diet. Of course you can't turn down mom's dinner, but maybe try to cut back on some of the spices and fish to see if that helps.
You mentioned that there is no school nurse and your friends have distanced themselves, but try to talk to the school counselor or a teacher that you might be closer to. Maybe one of them could write a note for your parents suggesting a trip to the doctor. You have every right to see a doctor if you feel something is wrong. I don't like the idea of lying to your parents, but maybe use your period as an excuse. Are you spotting at all, or has it totally disappeared? Use these concerns to get your mom to take you, and again, this is something that your GP should be able to address (as well as the smell, which an actual gynecologist might not be able to advise on).
Sorry for the wall of text! Good luck!