it sounds like it's just skin from your rapid weight loss, not fat that is making you uncomfortable. Unfortunately it will just take some time for your skin to tighten up, but adding some muscle will definitely help to fill out with some solid bulk. But to add muscle you need to change your whole approach.
First you will ned to start eating more. Not a lot more at first, but you need to cave a calorie surplus in order to build muscle. start with 12-15x bodyweight in calories. If you find you're still not gaining muscle, increase that byy 100-200 calories, if you find fat coming on, drop it by 100-200.
You need to get 1 to 2 grams of protein per pound of body weight. Muscle is made from proteins and you need to provide a constant supply. Lean proteins like chicken breast, eggs (egg whites), fish, tuna (cans of tuna are a quick and easy 37 g of protein), soy, nuts
Do NOT avoid all fats and carbs. They are both important so long as you eat the RIGHT fats and carbs. Avoid saturated fats (animal fats except fatty fish which are actually good for you) but unsaturated fats are good (nuts, nut butters, olives, olive oil, avocado, sunflower seeds etc.) Avoid sugars and starches (potato, white bread, white pasta), but make sure you get in complex carbs, ideally whole grains, brown rice, fresh fruits and veggies, oats and such. You may hate it, but broccoli is king. There's a reason that body builders live on chicken and broccoli.
How many days will you be able to go to the gym to lift each week? Do you have a workout buddy?