Yes, if you're undermedicated. You didn't include the reference ranges, but I'm guessing that your FT4 is bottom of the range? If that's so, you could use a dose increase, because thyroid hormone controls your metabolism. And yes, it's difficult to lose weight with a slow metabolism.

OTOH, undereating while overexercising will also lower your metabolism. The body slows your metabolism to conserve energy, because it senses you may be in starvation mode with limited food availability. If you further lower your calorie intake, you will further reduce your metabolism.

Finally, you cannot eat a lot of carbs and expect to lose weight, because a high carb diet creates insulin resistance, and that leads to weight gain. Whole wheat and gluten-free bread are still carbs. Protein and fats are essential. Weight gain is more often a problem of insulin resistance than hypothyroidism.