Hello and welcome to healthcare magic!!
is LMW heparin
and is given to prevent blood clots
it basically makes the blood thinner preventing formation of clots and complications and it has to be given sub cutaneously as far as site of injection is concerned you can ask the doctor if it can be given in thigh if the belly is not feasible and the bluish discoloration is because of bleeding at the site i think. and you can get a second opinion
from another gynaecologist or clinical haematologist if you are not happy with the treating doctor.