POor you, bad bronchiolitis is so scary. dd2 had it at 4 weeks old, and at the time probably 95% of the children's ward (and HDU, which she was in) had it too....and I heard over and over and over again that its very common for wheezing and coughing to continue for several weeks after the virus goes away.
Its true that I was also told that dd was at slightly increased risk of asthma and/or chest infections in future, but in her case so far so good. She has ENT issues, which make for troubled breathing, but nothing to do with her lungs.
She was also one of the lucky few who didn't cough after the virus went away...or wheeze, that I noticed (but she's a noisy breather, so who knows!), but my friend's ds, who had it less badly at the same time wheezed and coughed for weeks afterwards.
I'd give it another week or so, but do take the GP up on the offer of inhalers and see if it makes any difference, if no better soon or if you're worried. I don't know what the syrup is, but as far as inhalers go...their efficacy is part of the diagnostic process, IIRC, so might be helpful to know if they work at all?
Hope he's better soon, so far, it does sound really normal for post-RSV