A PCP (Primary Care Physician) would refer you to any specialists that you might need.
You must visit your primary care physician before seeing any other doctor for your tapeworm. Then, if it is beyond your primary doctor's ability to care for it, they will refer you to a doctor that accepts your insurance.
Your primary care doctor is legally empowered to do so. Every doctor can decide what medications she will prescribe.
Usually a primary care doctor can take care of that. If more help is needed they may refer you to an ear, nose, and throat specialist.
Primary care providers normally test testosterone levels.
Some specialists do primary care. Usually they take the role for people whose main concern is in their area of interest. Some, especially when first starting out, will do primary care to supplement their practice and plan to phase it out as they get busier in their specialty. As a personal perspective I often find it interesting that they would scoff at the idea of a primary care doc doing their job but yet insist that they can do the primary care just as well as people who specialize in that. If the doctor really was interested in primary care and wanted to do it he would have been a primary care physican. My personal advice it to get your primary care from a doc who finds it interesting and actually wants to do it.
Primary Care
The University of Washington does have a pediatric allergy department. You will have to have your primary care doctor refer you if you wish your child to be seen.
Primary care, orthopedics, rheumatology, and physiatry all take care of tendinitis. Ask your primary care provider for a referral appropriate for your situation.
Health care providers in family health, internal medicine, pediatrics, and gynecology all treat urinary infections. If your infections are frequent, recurrent, or complicated by other factors, your primary care provider may refer you to a urologist for evaluation.
Urologists evaluate and treat male fertility. Typically, any primary care provider can refer for semen analysis as a first step.
You may need a referral from your primary care doctor to see a surgeon. However, you may very well need some kind of corrective surgery. Have your primary care doctor take a look, and ask if surgery would be a good option.
Depending on where you live, a good weight control doctor will be easily found by asking your primary care doctor for a referral. Most doctors (maybe you primary care doctor too!) are specially trained to help patients lose weight.