Hi. I have 3 kids with asthma and allergies. It's miserable here, too! Have you ever considered immunotherapy (allergy shots) for your allergies? They've made a HUGE improvement in my 2 youngest children's asthma and allergy symptoms. Prior to shots, both had uncontrolled asthma despite aggressive asthma treatment. DD was miserable for over half the year and DS had severe sinus problems, including a failed sinus surgery (at the age of 4). They still have issues but instead of 4-6 meds daily year round, they now use just nasonex year round and add in more, as needed. Plus, they were both able to drop their inhaled steroid for their asthma!! DD had been on inhaled steroids daily for 3 yrs, DS for 5. Allergy shots don't work immediately, it takes a year or two to see good improvement, but they DID work well for my kids.
Also, it's pretty common to use both a nasal steroid spray and inhaled steroid (even the same brands). DD did not appear to have any issues using both. DS had some slowed growth/poor weight gain while on advair 500/50 and nasonex (he was 6). He's been off advair for a year now. He gained 15 lbs & grew several inches so it doesn't appear to have caused any long-term growth issues. We had no other issues using both.
Aside from allergy shots, my only other suggestion is nasal washes. They've helped DS and DH. We use to make our own solution but have switched to the Neil Med sinus rinse kit and like it.
As far as allergies causing asthma and vice versa, our ENT likes to say "one airway, one disease" meaning that the lower and upper airways are all connected so what affects one will usually affect the other.
Edited to add that I just noticed that you're starting allergy shots. Hopefully, you will have good results, like we have!!