The most important things aspects about treating Type 1 diabetes are seeing a doctor who is experienced in treating the condition(endocrinologist/diabetologist) and being well educated.
It is beyond the means of this forum to try and do a full education session, but regarding your daughter, normally a Type 1 diabetic is on a basal bolus insulin regimen, meaning a long acting insulin at night and then a short acting insulin before each of the main meals.
In your daughter’s case she seems to only be on a long acting insulin called humulin N, and I am unsure if she is on any short acting insulin.
With regards to the problems of the glucose levels, the main problem she is having is the lows, as the high readings are a consequence of overcorrecting the lows.
Her humulin N and eating will need to be adjusted to avoid the lows, and then the rebound highs should also to better. The thirstiness does suggest that overall control is on the high side, and so she may well require the short acting insulin as well.
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