Hi Rebecca,
If this is your first baby it is unusual for the baby's head not to be engaged at term. Are you term? There are really only two explanations for this:
1. Your baby's head is not in a good position for engagement eg direct OP. Optimal fetal positioning exercises should help - such as you have been doing.
2. Your baby's head does not fit in your pelvis.
Sorry to be blunt, but these unfortunately are the most common reasons in a first baby not engaging their head at 36-37 weeks of pregnancy.
If your baby's head is not in in the pelvis at all and your waters have broken, you should be in hospital, not at home. If you have been told that the baby's head is 'free' and not in the pelvis at all, and your waters have broken, you should be in hospital as this is a high risk of a cord prolapse. So I assume, by the fact you are still at home, that your baby's head is in the pelvis, just not deeply engaged. )Your midwife would not have let you go home if the baby's head was not in the pelvis.) If this is the case, carry on with leaning forward,feet behind hips, rotating hips, ride your birthing ball like a jockey - leaning onto a chair in front of you. If you are certain that your baby's head is approaching the pelvis in a transverse position (will only know by scan, vaginal examination, abdominal palpation for alignment of baby's back), you can practice deep squats. If you are not sure of baby's position, do not practice deep squats as you may force the baby's head into the pelvis in a poor position. This is something I have had success with, but I am a midwife and can be certain of the baby's position before giving this instruction.
Feel free to email me at vjkhodge@yahoo.co.uk if you would like to ask any further questions.
Good luck Rebecca.
Vanessa - Midwife and Birthlight Perinatal Yoga