What was your 25-hydroxy Vitamin D value? If not checked do it by asking your doctor.
Complication of taking Vitamin D supplement is hypercalcemia and that can bring many symptoms like increased thirst, hot flush, dry mouth, anger etc.
Hypercalcemia can also occur if you have excess thyroid hormone and Vitamin D can increase the symptom as more calcium get absorbed due to increased Vitamin D activation. So check your Free T3, Free T4 and TSH values. Anything close to high end of reference range (for TSH lower end) is abnormal.
Also worth to rule out hyperparathyroidism by doing serum calcium and PTH together. In such cases taking Vitamin D aggravate the symptoms.
They shouldn't make you ill like that, but you aren't supposed to take anything with your levothyroxine... It's supposed to be taken first thing in the morning, with a glass of water, then nothing to eat/drink for 30-60 minutes. You should wait, at least an hour or two before taking other medications, after you take your levothyroxine, if you can.
Vitamin D is a fat soluble vitamin, so it's recommended to be taken with the evening meal with some fat, for the best absorption.
If you aren't taking your levothyroxine properly, you might not be getting adequate absorption. Body pain can be a symptom of hypothyroidism.