Hair loss in a nuclear submarine?
If the question is related to exposure to radiation in a Nuclear submarine then the answer is valid for radiation exposure irrespective of the place. 

As you are aware there are many effects of radiation. Some of them are.


  
  Nausea and vomiting
  Diarrhea
  Skin burns (skin reddening)
  Weakness
  Lethargy and fatigue
  Loss of appetite (anorexia)
  Fainting
  Dehydration
  Inflammation of tissues (swelling, redness or tenderness)
  Hemorrhages under the skin
  Bleeding from your nose, gums or mouth
  Anemia 
  Hair loss (usually from just the scalp)
  Decrease in platelets (reference)
  


Of course there is no safe quantity of radiation that has been quantified (reference) and there are personal anecdotes by submarine officers about first hand problems they faced due to radiation (reference). However, since this is a career you chose, you can be happy that the amount of radiation that you would be exposed to has decreased over the years (reference). Since you are interested in the biological aspect of what happens in your body due to radiation, I quote


  When cells -- and what lies within them -- get exposed to radiation,
  components of DNA and critical proteins within the cell get all jazzed
  up (ionized), meaning that the electrons with our atoms get kicked
  out, causing the DNA strands to break and the proteins to cramp up
  (denature).
  
  Ionizing Radiation:
  
  
  Leads to the production of free radicals
  Breaks critical chemical bonds
  Leads to changes in cellular structure within irradiated cells
  Damages vital molecules, such as DNA, RNA, and other regulatory
  proteins
  
  
  Because our cells are mostly water, this ionizing radiation breaking
  H$_2$0 down is harmful to free radicals (H$^+$ and OH$^-$). While cells are
  damaged by free radicals all the time, they normally repair
  themselves, keeping the body healthy. However, high doses of radiation
  can damage the cell's ability to repair itself, and then all hell
  breaks loose.
  
  This shakes things up all over the body.
  
  Let's do a head-to-toe walk-through to investigate how high doses of
  radiation can damage the human body.
  
  BRAIN: Nerve cells (neurons) and brain blood vessels can die, leading to seizures.
  
  EYES: Radiation exposure increases the risk of cataracts.
  
  THYROID: When a nuclear reactor malfunctions, radioactive iodine (I-131) can be released into the atmosphere (this is one of the
  particles that hangs out in a "radioactive plume"). The thyroid is
  very sensitive to the effects of I-131 (in fact, I-131's affinity for
  the thyroid is used therapeutically to specifically attract radiation
  to the thyroid in order to treat thyroid cancer and overactive
  thyroid). When a healthy thyroid is exposed to I-131, it can lead to
  decreased thyroid function and, over time, thyroid cancer.
  
  LUNGS: When you breathe in invisible nuclear fallout particles, it can lead to lung cancer down the road.
  
  HEART: High doses of radiation can damage the cells in the blood vessels that feed the heart, reducing cardiac function.
  
  GI TRACT: Sensitive cells in the intestinal lining can be damaged, leading to nausea, bloody vomiting, and bloody diarrhea.
  
  REPRODUCTIVE ORGANS: Rapidly dividing cells (eggs and sperm) in the ovaries and testes can die, leading to sterility.
  
  SKIN: Rapidly dividing skin cells can be damaged, leading to skin lesions and burn.
  
  LYMPHATIC SYSTEM: Rapidly dividing lymphatic cells die and damaged bone marrow may have trouble replenishing these immune-boosting cells,
  increasing the risk of infection (reference).


Many jobs have occupational diseases connected with it so I would say don't worry about it too much, enjoy your job and keep your fingers off the firing mechanism.