Prescribed these as Covid has set my asthma off. Any idea if they'll help with the cough too?

I started getting Covid symptoms a week ago - congested, headaches, drowsy. I started getting a heavy chesty cough on Friday/Saturday. I tested negative on Friday and then Saturday. I'm a lot less congested now, but from Saturday/Sunday my breathing started getting very tight and my inhalers were not working at all, so got an urgent care appointment, and was prescribed these (previously worked very well and quickly for Asthma flats ups). I'm optimistic about it sorting the breathing out, but any idea if they'll help with the cough too?