Hey there - I totally understand, and it's the worst when the babies are sick. My 9 month-old is sick right now, and so is her 3 year-old brother. :( There's not much else you can do...my baby also doesn't love the bulb syringe, but at least she lets me do it. My first was like your baby, I could never use it on him because he would just flip out if I even tried. It does seem like a warm bath helps to get some of the gunk out. Before her bath, run the shower really warm for a few minutes to get the bathroom nice & steamy, then run her bath so that you're in the steamy bathroom during her bath. Also I'd run a water-only humidifier in her room at night. Otherwise it pretty much has to run its course. No, I don't think it's related to teething, I think she has a cold. HOWEVER, since she also has a fever, I'd definitely make an appt to get into the doctor tomorrow and make sure she doesn't have an ear infection or anything in her chest.
Good luck & don't worry, she'll get over it!