Hi,yes your haemoglobin is borderline..as you are putting weight,I would suggest you to do thyroid function test ,also check vit b12levels,

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Your heamoglobin is not very low to cause dizziness it is on borderline, though we may need to increase its level. But before starting iron supplements there are other investigations that we need to do such ferritin levels, total binding capacity, reticular count, serum iron levels. There are many causes of dizziness, I agree one of the cause is low hemoglobin level, but your hemoglobin levels are not very low to as such cause so much of dizziness, so we need to rule out other problems that can cause dizziness and you said weight is also increasing so low thyroid problem should be ruled out in you as it causes weight gain and dizziness