Hi Lab
I'm in the Uk so cannot recommend any doctors in your area, but I'm sure there will be loads of Male Health Physicians or similar, in your locality.
240ng/dl is pretty low and if you feel as rough as you say you are, then I think it does warrant further investigation. Unfortunately, I'm not a Platinum member and so cannot view the details you attached.
Did your blood work include: LH/FSH, and free or Bioavailable Testosterone? Did they at all measure your levels of prolactin, progesterone, and/or oestriadol, oestrogen (E2?
Basically, if you are hypogonadal it is important to understand why, and hence, what sort of hypogonadism it is you have. There are two distinct types: Primary Hypogonadism, and Secondary Hypogonadism. A third type, and somewhat rarer than the other two is called Central Hypogonadism, which is essentially a combination of Primary and Secondary Hypogonadism.
Primary Hypogonadism: is low testosterone caused by a malfunctioning testicle(s). The gonads aren't capable of producing normal levels of testosterone. This is usually the type that necessitates hormone therapy in the form of gels, patches, pellets, or injections of testosterone.
Secondary Hypogonadism: is also known by various other names depending on specific diagnosis: hypogonadotropic or hypopituitary hypogonadism. These types are primarily due to the malfunctioning of the pituitary gland. The pituitary releases the hormone LH (Luteinising Hormone), which is the hormone produced to instruct the testes to release testosterone. The same gland also secretes FSH (Follicle Stimulating Hormone), which is responsible for ensuring testicular production of sperm. A pituitary related issue that results in failure to produce adequate mounts of either hormone LH/FSH, will likely cause low testosterone and symptoms thereof.
Secondary Hypogonadism usually responds well to exogenous testosterone supplementation, like in Primary Hypogonadism cases. However, the good news is, if you are diagnosed as Secondary Hypogonadal, patients might be able to employ Clomid (Clomiphene Citrate) as a therapy. Clomid is a drug which increases production of LH and associated hormones, that, in turn, instruct the testicles to produce testosterone. Many doctors are now trialling this version of therapy on their patients, usually with outstanding results. I know of three Secondary Hypogonadal males who failed to respond well to testosterone therapy, but did massively well on Clomid.
Clomid is also cheaper to buy, easier to administer (tablets) vs. injections, and overall safer to take than other forms of HRT. Clomid also has no effect on the production of your natural testosterone upon discontinuation of the medication. However, hypogonadism is usually a life-long condition, and Clomid will probably have to be used for many years.
Simply put: if you are found to hypogonadal and requiring treatment, find out which type of condition you have. If it is a pituitary related problem then Clomid would probably be a safer, cheaper, and much more effective treatment option than testosterone therapy, which you are averse to.
All the very best.
Craig