Yep, soreness is not a factor for effectiveness. Athletes are rarely sore. Your body adapts to fitness. Some people feel sore after everything they do. Some never feel sore at all. It all depends on the person.
Same with sweating. A lot of people believe the more you sweat the better. But that's not true. I amy sweat a lot and you may not sweat at all. But we could both be working out at the same intensity level.
The best factor in determining if your exercise and nutrition program is working is to test your body fat %. Most gyms do this for their members at no cost.
Pilates works the core area. So your stomach may look and feel better afterwards. The ball should give you just as good as a workout. The Plank pose is best, IMO. You can do do as many sets as you would like for the ball. But I'm getting the impression that you are just working the abs?? Is that the correct assumption?
If so, you should really get involved with a full body routine. It will help you so so so so so so much more than just working the abs. Since you are just beginning, I would stick to doing the . The same goes for the abs. Do 3 sets of an ab exercise. That can be divided up into 1 Plank pose, 1 set of Reverse Crunches and 1 set of Stability Ball Crunches.
Your nutrition program can use a lot of help- sorry to say

My comments are in brackets next to your meal plan.
Breakfast 8:15 - yogurt - 140 cal [Add protein here]
Snack 10:15- Weight Control Oatmeal made with splenda - 160 cal [Add protein here]
Lunch 12:45- Turkey Sandwich on Wheat w/ cheese - 350 cal [Not bad]
Snack 3:15- Atkins Morning Start Trail Mix Bar (11g protetin) - 160 cal [Ditch this all together. Try cottage cheese and a piece of fruit]
Dinner 7- grilled chicken breast and veggies [Good]
right now i'm in school so no time for dinner so i've been having a snack at 6 with triscuits,turkey, and cheese (like 200 calories) and then 200 calories of cheez-its during class at 8pm ... [Ditch the cheez-its. Try a protein bar if you need something to munch on. I'm not a fan of protein bars, but they have their place... this is a place for them. You have dinner at 7pm, but then say you don't have dinner because you are in school... so you eat triscuits, turkey and cheese. I'm not sure which one you are doing right now.]
Re-read those steps to fat loss again. It mentiones that each meal should have a carb and a protein. It also metions the importance of a full body strength training program.