Getting Rid of Blackheads

Skin problems are a symptom of thyroid disease. I have skin problems - dry skin, eczema, adult acne. Add menstrual problems due to my thyroid disease (and y'all know about acne problems throughout the menstrual cycle), and I'm just one big, walking skin problem.  How can you have dry skin AND acne? I have no idea!  What about blackheads?  Is that a thyroid thing or just a skin thing? 

How do you get rid of blackheads?  I have two on my face that are not on top of the skin.  They are under the top skin layer.  Can't even pick them out!!  (I know, you're not supposed to pick them but who can resist when you just want them GONE!?!)  How do I get rid of them?