I think your skin issue might be related to muscle loss from being underweight. The best way to tighten skin is to gain muscle. Don’t worry about becoming ‘bulky’, you won’t. Eat maintenance calories but focus on upping your protein, fats should be a part of a healthy diet. Try an elimination diet to see which foods trigger your digestion issues. Sugars and dairy are digestion disruptors for me. It may be that you are eating too little, and that is causing your digestion distress. Try whole, unprocessed foods with plenty of protein and nutrients.
Im concerned for you. think you she seek the help of a trained professional like a dietician or physician. You are seriously underweight with a BMI of 15.. eating a very low calorie diet, and asking about adding restrictions, and mention specifically not gaining any weight when you recognize you are outside the healthy range.
Outside of that, you cannot gain muscle in a calorie deficit under these conditions. And at such a low body weight you cannot put on muscle without gaining weight. Maybe you can add muscle without gaining fat but you need a calorie surplus to build muscle, and adding muscle means adding body weight. And those extra calories required to build muscle have to come from the food you’re eating when you don’t have excess body fat stores to tap into.