No period need to gain weight HEALTHILY

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I have gone a bit crazy with my weight loss and am now about 143 lb at 5'9.5. It doesn't sound too bad but for my body it is too low, I look too thin and gaunt, my period has stopped and I am starting to feel quite brain foggy and even having panic attacks due to not having a menstrual period and being terrified as to what is wrong with my body.

After seeing my doctor she told me I need to get up to 150-155lb to regain my period. That was the weight range that I maintained for 3 years effortlessly while still eating junk food, ect. I have been losing weight by reducing my carbs to under 10g per day. As I result my weight has dropped to 143 (I was 165 lb after recovering from an ED and regaining all the weight plus 10-15 extra). My doctor was happy with my weight at 150-160 but 150-155 lb for myself is ideal.

However I do not want to just gain fat. I want to be slim, toned and lean with muscle. I need help though to gain the 10 or so pounds I need to gain healthily and to make most of it muscle (7 lb muscle/3 lb fat would be ideal) but I need some help. I don't want to just "Balloon" up in weight and become a chubby girl again I want to do it so that I will remain essentially slim/tiny but at a healthier weight.

I do think my body fat is around 23-25%. I have pins for legs but chubby thighs and butt and a block waist. If i had it my way I would lose waaay more weight but my body is screaming quite clearly.

I still want to keep my carbs low. Not under 10g though as I started experiencing depression, panic attacks and constant anxiety. I ate 35g carbs today of nuts, meat and green veggies and I feel much better and in a lot less of a fog. I think if I stay around 35-50g per day that still would be low carb correct? I want to eat low carb so that I do not constantly feel bloated or sick like I do when eating lots of carbs and sugar and so the weight gained is as much muscle as possible and won't make me look like I just gained 10 lb.

I want to have a bigger rear-end, more toned arms and legs and my stomach is not too big. It remains pretty flat with low carb eating so I am not too concerned about it. I want to look strong but fit and slim. Not unfit and untoned like I previously was at 150-160 lb.

What do I do? If I eat low carb but at a surplus and do a carb up every 2 weeks I will lift weights heavy 3x a week, use my weighted hula hoop 3x a week and go for daily walks. Will that build me muscle to give me a leaned, slim look?

Btw I am aware this will take quite a while. Probably 3-6 months.