If borax is drying to nose membranes, try to reduse the dose you take. Or take it 2-3 times a week, not every day.
It works well also in small dosages.
Also some aloe gel are soothing for dry nose.
I once tested borax by taking way too much of it for 10 days; if I recall right I took 6 capsules filled with borax (almost a gram in each!)- a dry crusty nose and dry skin was the only overdose symptoms I could notice. The symptoms was gone 2-3 days after I quit.
After that testing it was easier to dose the borax; I found my limit so to speak. It works fast; It also has a short half life; some 20 hours, similar to iodine. Its effect on bladder issues are amazing.