Understanding and diagnosing Low testosterone require sound knowledge in this field and unfortunately many Physicians just look at the reference levels and say its ok. In reality it is NOT.
You have every right to ask for through examination that should include LH, FSH levels, SHBG, along with FBE, LFT, and also U & E, cholesterol, and Blood sugar levels. and on top of that you also need to have your blood taken in the morning at least on 2 different times. Testosterone peaks in the morning and decreases during the day. 8am-10am is preferred for LAB work.
Your doctor needs to rule out if its a Primary/Secondary issue for your Low T, if LH, FSH is low normal then he/should also check prolactin levels and if prolactin levels are high then MRI is needed to rule out any pituitary adenomas. If LH/FSH is elevated then he/she should check your Testes itself along with other genetic disorders to rule out other causes.
So get your blood work done first then go from there.
Cheers
Sunny