catarrh +++ in 5yr old

My daughter who is 5 has had almost constant catarrh discharging from and blocking her nose for about 6 weeks. This is complicated by the fact that she has Down syndrome and pulmonary hypertension requiring the use of continuous oxygen which then dries up the catarrh in her nose thereby not letting the oxygen to get to her lungs. We did take her to hospital for 3 days where she was treated with broncho dilators, saline nebuliser and chest physio but the problem started again a few days after discharge. The mucous is very thick and a yellow/green colour. She is worse at night and mornings until about 1pm. I think but not certain that exposure to cold weather makes it worse. She sleeps well at night despite the problem and has energy during the day (more than can be said for her parents!!). She has had no other symptoms such as fever or pain that we know of. She was given antibiotic (despite no findings of bacterial infectio) in hosp for 5 days which for some odd reason always seems to help her oxygen levels. She recently (3 months ago) developed the strange habit of licking or even biting mortar from a part of a wall in our appartment which she tries to do about twice a week. Before this she would try to eat lumps of plant compost from the plants in the appartment. She has hypothyroidism which was treated homeopathically until her TSH levels began to consistently rise. She has always had problems with her bowels which is managed through diet and movement but recently (past 4 or 5 weeks) her bowels have slowed down again and she becomes constipated more easily again. She has always grinded her teeth together but does this almost all of the time now (for the past 4 weeks or so). We feel her lungs are probably very congested but the phflegm is not loose and she does not cough productively very much. We are continuing chest physio and sometimes saline nebuliser for this. We would be very grateful for your input regarding any homeopathic remedy or remedies you feel might help her situation.
Kind regards,
Mariel