Im 25 yrs old, 5'5, female, size 12-14. Ive lost 11 pounds so far and have 15 to go.
Im doing low carb and working out 5-6 days per week for 45 minutes per day. I eat everytime Im hungry (breakfast at 7, lunch at noon, dinner at 6) and thats usually all I eat because Im not hungry any other time. I think the problem is Im only averaging 1100 calories per day but Im getting 40 carbs/day.
For the past few days after I work out, I feel very sick. Light headed, weak, etc. I actually collapsed in the shower tonight and my husband had to finish washing my hair. I know I need more calories but is this why I am feeling sick? How do I add more calories without adding simple carbs?

Add low GI carbs. Have a piece of fruit after your workout. Even on a low carb diet, some carbohydrates after your workout are imperative to replenish your glycogen. It sounds like you're getting extremely hypoglycemic and you have to get it back to normal. Carbs right after your workout are the best time to have them as they will be shuttled into muscle tissue rather than stored as fat.
And DEFINITELY add more calories. Not for the hypoglycemia, because you're probably causing a starvation response and seriously hindering fat loss. Add some healthy fats or veggies or protein. Some snack between lunch and dinner would be perfect.