Hypothyroidism is full of some really fucking harmful quackery on the Internet. Please avoid those bad websites. You're right that it needs careful monitoring to get the dose right.
A general supplement of vitamins A,C, and D is probably not harmful. (Do not overdose on vitamins. They can be toxic and can kill.)
And now some other stuff:
Work towards getting better food and some exercise into your life. Set small, realistic, achievable goals. Give yourself credit when you meet those. Fresh fruit and veg are not too expensive and will make a difference. Good food will help you feel better. Exercise will help to reduce stress.
Investigate some course of CBT. This can be done by yourself from a book; or online; or you can get some guided course. In the UK it's available free (you ask your GP and say words like "CBT" and "IAPT" and "Primary care mental health services" until you get it; or you can sometimes self refer.) In other countries you'll want to find out who registers therapists and then search for a therapist with that registration.
It is surprising how much difference a short course and hard work can make - 8 weeks at 1 hour per week can really help a lot of people.