Concerning your bowel habits, it sounds like you may have Irritable Bowel Syndrome. Small balls of waste with mucous is a solid indication of IBS. This is usually cured up by introducing fiber into your diet, i.e., fruit and vegetables. Also, if you are a meat eater, it would be wise to cut back. Another indication that you may have IBS is that it tends to go along with acid reflux disease, which is annoying when you lay down. You have so many symptoms, that it is hard to tell which one is causing you the most problems. However, I would suggest working on your bowel issues. I believe that diseases start in the colon. You can do this by increasing your intake of vegs and fruits, and decreasing sugar, meats, milk. This is just a suggestion. Try it, you just may like it. GOOD LUCK
I agree that it sounds like you are anemic. Could be low iron or low B12, most of which also comes from animal products (meat, dairy and eggs).
Yes, you can lose weight, when hypothyroid; your bowel issues could be from hypothyroidism or from something else. Diabetes can also cause weight loss and the shaking/weakness.
If you are hypo, your "female" hormones could be messed up as well, which could cause pain in your lower abdominal area, along with some of the other symptoms. Constipation could also cause the pain.
The choking feeling could be anything from swollen thyroid to stress.
You really do need to go to the doctor and get checked out. There is lots of blood work to be done, that will tell you what the problem is. Most states/counties have a Public Health Dept for people who can't afford a doctor. They may treat you for free or treatment could be on an income related basis. Talk to your parents about all of this, as you need to find out what the problem is and get it treated, in order to prevent it getting worse.
Sounds more like you are anemic. Especially if you are tyring to be a vegan. Vegans need to eat far more plant food to get iron, and most iron from plant foods is not obtained by the human body.
You can still lose weight being hypo but not usually.
Your bowel motions sound like either a coeliac, diverticulitis or Chron's disease.
The ovarian pain could be an ovarian cyst.
You need to be checked out thoroughly. Make sure you mention everything you have here, to the doctor. If you can't afford a doctor then you won't find the answer. We can only guess at what is wrong. You need thorough blood tests.