I would invest in a high strength stain removal spray. I suggest Shout or Spray and Wash. Then, spray the arm pits of your shirt (spray both on the inside and outside) then wash your clothes. This should get the stains out.
I recently read in an article that to get stains out of clothing that comes from deodrant and sweating combined is to soak in vinegar and wat for about ten minutes then blot the stain with a paper towel.
Apply little lemon juice or Vinager on affected part and rub well. Hang cloth in open place. Mix washing powder in luke warm water and put the cloth in it. Soak the clothes in the above mixed water and keep for some time and rub the cloth well. Wash the cloth as usual. You will see the problem is solved.