I think that was a big mistake we made. It was a lesson for us. We were still feeling dizzy when we reached Ringhim that night but after having cups of warm milk and tea we were all good again.
Ringhim was also a part of North Sikkim but less cold as compared to Lachung and Lachen. We stayed there for the night before we returned to NJP for our way back home. We also managed to get the view of the Kanchanjanga ranges.
The overall experience was great and I will recommend everyone to visit north Sikkim who do not suffer from any breathing problems or high altitude sickness.
Unfortunately we couldn't visit Kala Patthar and Tso Lhamo lake. Construction were going on in Kala Patthar and from March 2020 it will be again open for the civilians. While we didn't have the permit for Tso Lhamo lake which is the highest lake in India at a height of above 19000 ft.
Itinerary for North Sikkim : 4 days/ 3 nights