Thanks for the query to H.C.M. FORUM.
As you mentioned in your query that your sister developed bronchitis
and shortness in breath.
For restoration of breath some drugs ( bronchodilators ) were used ( these drugs were necessary for treatment ) and due to this some vessels ( minor) ruptured and hence she developed blood from the eyes.
This is a normal process and as this was also advised by your treating physician, so need not to concern.
Otherwise your sister is alright.
In my opinion your doctor is doing well and everything is under control.