i would advise is to take regular breaks from your studying, eat regularly and make sure you take time out to relax and wind down each day.
whatever you decide, the most important thing is your health. maybe consider how much longer you can carry on the way you are with work and studying. if you don't feel you can last the distance, then something has to give - don't compromise your health in a bid to 'take on' this illness.
i know it's not what you want to hear... but may be even part time with out breaks is too much... can you suggest to them that you do it part 