Brith control has been known to have various side effects and it can differ from person to person eg: low libido, weight gain, messed up hormones, hair shedding, extreme tiredness. all the symptoms are as a result to hormones becoming imbalanced.
Not all doctors check that the pill they are putting you on is right for YOU. A lot of doctors simply give out whichever brand of pill without caring whether it's right or not. Some of the newer brands of pill are high in estrogen or estrogen only and this often causes hormonal issues due to the imbalance of estrogen to progesterone ratio.
As for the the deficiency in testosterone, that will definitely cause low libido without question. Your doctor should know this and be doing something about it. Your doctor should either try to find out what is causing the low testosterone or put you on a bio-identical cream to help lift your testosterone levels.
Low testosterone 'can' also lead to: fatigue, mental 'fuzziness', memory problems, depression, poor concentration, heart palpitaions, vaginal dryness, aches pains, thinning skin, bone loss, muscle weakness. You wont necessarily have all these symptoms, but you likely feel as you have more than just the low libido.
I myself had excess testosterone, but that was linked to my thyroid and adrenal issues and it self corrected once i began thyroid and adrenal medication.
Has your doctor tested all your other hormones? Just remember, when doing hormone testing you should do the blood test first thing in the morning eg: between 8am - 10am. Blood should be drawn after day 8 of your cycle and preferably before day 20. A serum sample is preferred over a plasma blood sample.
When there are testosterone problems your doctor should check your adrenal function and growth hormone levels too.
When you have low testosterone you shouldn't do any high intensity/volume work outs instead do lighter training to give your body a recharge. Zinc and magnesium supplements help testosterone levels too.
People can have varying libido levels, but when you have been tested and your testosterone is definitely low then your doctor should be doing more than simply sticking you on another form of birth control. If this is the case i'd be looking for a new doctor who has an understanding in hormones. Letting something like this go can lead to more and more symptoms over time.
Good luck and hoping you get some help soon