How can I get rid of this mole? I've gotten rid of it before but it came back. Whenever I squeeze it whiteheads come out (photo)

Based upon your history and the picture you provided this spot on your nose may be an inclusion cyst.  In order to fully remove the lesion my recommendation would be to have an excisional biopsy.  This means that your doctor would numb the skin with local anesthesia and surgically remove it (cut it out).  This way you can have the pathologist fully evaluate it and let you know what it was for sure. It would also be completely removed at that point.  You would have a few stitches but trading this spot for a small scar may be worth it for you. 
Not everyone is a good candidate for this treatment so please see a Board Certified or Board Eligible Plastic Surgeon to evaluate if you may benefit. Good luck!
This content is for educational and informational purposes only. It is not a substitute for medical advice, diagnosis, or treatment provided by a qualified healthcare professional.  You should always seek the advice of your physician or healthcare professional for any questions you have about your own medical condition. 

Getting rid of that ugly bump on the nose is easy and quick and so worth it under local. Do it today and be so happy you did.