Hang in there, mama! You're doing great!
First off, I have an asthmatic "child" (she's 29 now), another child with the rare to occasional asthma issue and have asthma myself. Let me tell you, it's a great deal more difficult to watch your child during an attack than to deal with one of your own.
My advice: for a 3.5 yo, definitely the nebulizer at the first sign of ANY issue. You can use it up to every 4 hours, I believe. Stay with that, even if you don't hear wheezing. The idea is to prevent it from getting worse, not just react once it's an issue. So, it's great that she used it this morning and it helped. If it's been more than four hours, do it again.
If she's not on any preventative medicine, talk with your doctor on Monday about starting something & keeping her on it through the winter. Most of these contain a steroid and are perfectly, totally safe -- much better for her developing brain than being deprived of oxygen because she can't breathe properly.
Keep in mind that the preventatives take upwards of a week or two to really help. Once you start on it, keep taking it -- even if there are no cold symptoms. Also, it's totally OK to use the "rescue" medicine (usually albuterol; brand name Ventolin) in the nebulizer (or an inhaler, when she's older) even if she's taking the preventative. There will be times when she needs both.
Stay away from most cough & cold medicines for an asthma cough. In my house, we find Sudafed helps with the typical cold symptoms while not making the asthma cough worse. Straight Robitussin also seems to help.
Steamy showers are bad. Cold outside air is good. Many nights I'd throw a comforter over my daughter and we'd go sit outside on the back steps, watching the stars and the airplanes.
DO NOT express any concern or anxiety to your daughter. Be sympathetic and understanding, but always project to her that everything is fine and you've got it under control & that the medicine will help. Nothing makes asthma worse like anxiety, and yours will breed more in her. Sing songs to her, be easy and calm (I remember times when i had to, as they say "fake it till you make it" to help my daughter relax -- but it worked).
Hang in there! You're doing the right things. Keep up with the nebulizer. Call her doctor on Monday & ask for a preventative if she doesn't have one. Consider a sick call if you think the nebulizer isn't helping enough.
Good luck!