What kind of doctor should I go to concerning issues of premature ejaculation?

Internist or psych! Either one can help. Serotonin re-uptake inhibitors have been used quite successfully in dealing with premature ejaculation. These are drugs like Prozac and celexa, or zoloft (sertraline). There are 23 published studies documenting reasonable success between 2009-2011 on pubmed. I have used it effectively in my patients.
A Urologist. The mainstay of medical treatment for premature ejaculation has been ssri type antidepressants. Paxil (paroxetine) 10-20mg is most often used. It can be taken about an hour before sex or or on a daily basis. It stays in your system for a few days and can have other side effects as a result. In the usa watch for a new short acting drug (dapoxetine) this year. It will be just for premature ejaculation.