It could be low blood pressure and low blood sugar.
Try to make sure you drink enough, you need extra fluid when BF. Too little fluid can contribute to your BP getting low and dizziness.
You also need about 500 cal extra a day (I read 300 in PG and 500 for BF), so that equates to at least an extra bowl of cereals a day. Just be careful to use it wisely and not on an extra choccie bar as that wont help how you feel! I know in the early days it can be hard to find time to eat properly but it is really important as your resources will go into making the milk. If you don't have sufficient nutrients in your body to put into the milk, not only will you drain yourself, you might not pass the required vitamins and minerals onto the baby.
It sounds as if your blood sugar may be dropping, that can happen if you don't eat enough foods which release energy slowly to keep you going between meals, it's a problem I've suffered from since being a kid. Things like bananas and pasta are great and release energy slowly but other fruits like oranges and apples (and also sweet foods like chocolate and sweets) can cause a sudden sugar spike followed by a huge drop in blood sugar which can also leave you feeling shaky.
If you still feel you are having issues after making sure you are eating and drinking well, keep a food diary for a few days and note when you feel this way so you can go to the Dr for some checks. Hope you feel better soon x