Will shots of human growth hormone help me build muscle fast?

Not approved. Growth hormone is an anabolic substance, meaning it promotes the production of protein. It is not approved for such purposes, but athletes having using it as a performance enhancer and to quiken recovery of injured muscle. There are no scientific studies verifying this since it is not approved for such. Beware of going against nature's design, she will ask for payback.
Doping. Growth hormone does promote growth of lean body mass. However, gh can have terrible side effects when taken inappropriately: acromegaly, diabetes, raised intracranial pressure, very possibly higher risk for malignancy because gh may stimulate growth of cells with cancer potential. Not safe at all for someone who wants to add muscle and has no physiologic need for additional growth hormone.

Related Questions

Should I take human growth hormone therapy if I want to gain muscle?

No. Human growth hormone (hgh) has not been proven to produce significant performance enhancement and serious side effects are associated with its use including acromegaly, arthritis, carpal tunnel syndrome, and cardiomyopathy (the leading cause of death in HGH users). Most athletic organizations ban its use by their athletes.
No. Administering gh for the sole purpose of muscle expansion is not physiological and likely to cause harm more than good.
HGH vs testosterone. Hgh has been used as the perverbial fountain of youth by the "rich and famous" for decades. Only more recently has it been fda approved for usage in adults shown to be deficient. Cost is still prohibitively expensive, and not covered by drug plans. Bodybuilders at the professional level use far higher dosages than the general public, meaning megabucks! Testosterones are a better choice.