How would I know for sure if I have a nutrient deficiency?

it is probably best to go to a doctor, despite the expense. i would suggest taking zinc, except that if you don't have an actual problem you could suffer from a zinc overdose which can be dangerous. if you don't want to go to the doctor (which you really should) you should consider eating more foods containing high amounts of zinc. that way you can help your problem if you have one, but you don't have to risk a possible zinc overdose.