Don't fret, needing vitamins doesn't mean you aren't eating well. Even if you eat a perfect diet, there are other reasons you can be depleted of vitamins, either because you use up your stores, or because you don't absorb nutrients from food well enough. Things like illness, injury, surgery, sleep deprivation and certain conditions (like thyroid disorders) will put you at risk for deficiencies. And of course, pregnancy and breastfeeding takes a lot out of you.
Plenty of medications can deplete you of vitamins too. Antacids are the absolute worst for this. Here's a great resource about drugs and vitamin depletions. You can look up any medication you're on and see what various nutrients may have been affected. http://umm.edu/health/medical/altmed
Also, people just don't eat organ meat like we used to fifty years ago. Beef liver is arguably the most nutrient dense food out there. The best source of vitamin A and b-vitamins.
If you have a thyroid issue, even a well controlled one, you probably experience both absorption problems AND nutrient overuse or underuse. It's kind of the nature of the beast. Even a few days of being hyperthyroid can deplete you of thiamine. And it's very very dangerous to run out of thiamine. People who die from hyperthyroid episodes are essentially dying from acute b-vitamin deficiency.
For the absorption aspect, I take a digestive enzyme supplement which helps to make sure I break down my food and get all the nutrition out of what I eat. I also started taking an apple cider vinegar supplement with food, because low stomach acid (very common with thyroid conditions) means you also don't get the nutrition from your food. Certain vitamins need a high acid environment for absorption, like iron and B vitamins.
Let us know how it goes!
If getting tested isn't going to happen for you, you could very safely start with a strong multi-vitamin, maybe even a prenatal for the extra iron. And add a B complex with at least 25mg of most things. Plus a separate B12 by itself, something with at least 2500mcg. In addition, take a cod liver oil with a lot of vitamin A, so you get something like 10,000 IU a day. Especially if you have poor night vision.