3-year toddler with excessive clear mucus

Hello,

My daughter has just turned 3, she is still breastfeeding (and while she breastfeeds a lot, it doesn't disrupt her eating, and she eats very healthy foods). Her father is an allergic/has mild asthma. My daughter snores heavily at night, and whenever she catches a cold, the excessive clear mucus lasts for over two months. She is a mouth breather, but when she breastfeeds at night, she seems to be able to breath through the nose for some periods. She sometimes has a bit of sleep apnea, although the pauses in breathing don't last long (4 seconds, on occasion, a bit longer).

Since her mucus was changing color about a week ago (greenish/yellowish), she had a nose swab which came back positive for streptococcus pneumoniae. Therefore, she is now on the fourth day of amoxicillin 750mg (5ml twice daily) as directed by her pediatrician.

She is also on nasal budesonide shots (1 in each nostril, in the morning and at night).

I wouldn't want her to continue to have to take antibiotics and this is most likely allergies, given her family history on the side of her father. She hasn't had any allergies testing yet.

What can I do to make her more comfortable? She speaks amazingly well since she was very little and she conveys to me that she can't smell things and wishes for her nose to be cleared up... I'm heartbroken I can't seem to be able to help her. Please help us.