It is possible to adjust your posture/position of the head etc so that the "sideways-ness" is minimised, and you give yourself more room to breathe. One thing I notice when teaching is the tendency to look straight forward and then bring the flute up to meet your mouth which means your arms are scrunched right across your body and your chest is constricted: it doesn't work! It also makes hand position really weird. You need to adjust the position of the flute so that you can actually breathe and move your hands freely or you make everything more difficult! Without a specialised mouthpiece like the Drelinger one or that chap from holland (whose name I always forget) the side held nature of the flute will always make life more difficult, I guess, but there are ways to minimise the problems & have as natural a posture as possible!
The other thing to do is to check you are breathing properly and deeply, and supporting the sound, and practice long notes/developing your ability to use your breath efficiently.
Try not to raise your shoulders when you breathe in...
Can't think of anything else off the top of my head

one good book on the subject is the Trevor Wye volume on breathing. (I think it's breathing and something, but forget what the "something" is!)
There are many experienced flute teachers on here who will probably be able to give more help.