Its a very strong plant so don't worry. All you need to do is ensure you don't leave any of the rot in the plant. You say that when you cut back you noticed no rot and only healthy tissue. That's a very good sign. (No need of further cutting of tissue and hanging upside down).Allow that to heal and form a light callus. Then re pot. Make sure your medium is free draining. Water once a week. Ensure your Adenium is placed in a position where you have maximum sunlight.

All the best Patzii!

Thank you very much for your kind advice. Upload some photos here for better illustration and currently I'm hanging it upside down.

Hi Patzii! Yup your Adenium looks stressed! Keep it hung upside down only for a couple of weeks. When you repot please ensure that the caudex( fat portion) is placed above the soil level. I would also advise you to prune the 3 branches by 4-5 inches and make them shorter. If you dont prune them they tend to get too long without proper mass. In case you have a rot somewhere... please cut it off now. Use some fungicide (neem oil is a natural fungicide).Ensure you use a free draining potting mix. Water once a week.

Good Luck!