Are there any other options that may be free?
Yes. This isn't a joke. I've read the thread and see what is going on, and see lots of good advice given here on the psychological side, and I understand that your parents have a certain view and resistance to certain kinds of counselling or therapy.
I'm coming at you from a completely different direction, and I think in your case this may well help you better than the other options, and may be more doable, because it doesn't require anybody else's cooperation.
Let me ask you five simple questions:
(1) Do you like salmon?
(2) Do you like oysters?
(3) Do you like plums, prunes, apples or almonds?
(4) Do you like asparagus?
(5) Do you drink coffee, tea or soda pop?
Since you're not getting anywhere on therapists, and you're suffering with anxiety, and you are in danger of telling people about it and getting hurt further, here is what I recommend you do - it barely needs parental permission.
First, if you drink anything with caffeine in it - stop. Don't go cold turkey, you'll get a terrible headache for three days. If you drink soda pop, switch to coffee for a week. If you drink coffee, switch to tea. And if you're just a tea drinker, switch to water or coconut water. Get the caffeine out of your system, and get the fake sugar out of your system. These things are known to cause anxiety.
Second, next time your family makes a grocery run, go with them and buy a can or two of oysters. Smoked oysters are fine. Oysters are full of zinc. Eat 2 or 3 a day - no MORE than that, because they are SO full of zinc you'll end up accumulating too much of it in your system if you eat more than three a day. Sure, you could eat 21 a week, but don't. Don't eat a can a week, eat a few a day. Two things will happen for sure. First, if you have acne, it will clear up rather quickly. If you're a teenage BOY it will really clear up acne (no need to discuss the mechanism as to why). Second, most Americans are zinc deficient, zinc deficiency makes us prone to skin breakouts and nervous disorders. Oysters have more zinc in them than other food in the world (and they taste good). Get the caffeine out of your system and the zinc into your system and you will feel better mentally.
Third, buy some cans of Sockeye Salmon. If they don't have Sockeye, buy Pink Salmon. Sockeye tastes better, but getting the salmon is the important thing. Eat at least 4 ounces of it (that's a little over a half a can) every day, or a can every two days). This will fill your Vitamin D requirement, and your Omega-3 fatty acid requirement. Vitamin D is a hormone and you need a lot of it. Vitamin D deficiency is a well-known source of anxiety and depression, and most Americans are deficient. Omega-3 fatty acids, and particularly the DHA and EPA in fish oil are tonic for the whole nervous system. They will make you healthier and make you smarter. Salmon is very high in Omega-3 fatty acids. Sockeye salmon has more Vitamin D in it than any other food in the world except for Cod Liver Oil (which is nasty).
Fourth: Eat asparagus. Asparagus has been eaten as an anti-anxiety food for a long, long time.
Fifth: Eat apples, plums, prunes, cherries and almonds.
A can of oysters is $2 and will last a week. A can of Sockeye salmon is about $3.50, and three will last a week.
If you do this, even if you never get to see a psychologist or therapist, chances are you will have clear skin, a much sharper mind, and your anxiety will diminish substantially.