The ingrown hair on your stomach can be possibly furunculosis or a boil that is infected by a bacterium called streptococcus aureus due to a trapped hair follicle. The symptoms are similar to what you mentioned like inflamed tender skin, swollen, hard and painful with pus formation. The pain or swelling is basically due to the pus or the infected fluid in the infected ingrown hair. Yes if you can manage to squeeze the inner contents or pus which has caused the swelling it would help decrease the pain and make you feel much better.
As you have described I feel that the boil is large enough and ready to drain its content, so just press with your fingers (don't use nails) and drain the pus out. Along with the pus you will observe a hair will also come out. Clean the area with a fresh cotton ball as this will avoid any infection from spreading further. If the ingrown hair is too stubborn to manage it at home level then because it is placed on the stomach and the skin is very tender then considers taking a professional help. A health care specialist would easily drain the pus by making a small cut or using a syringe and needle to drain the pus out. Once the liquid is out along with the hair the skin generally heals on its own quickly.
answered by Dr S