My cat has an ongoing cough. He has been diagnosed with feline asthma. He gets regular steroid jabs and they help control it. No blood though.
I started him on daily inhalers. Actually giving the inhaler was simple. Catching him to give him the inhaler was a nightmare.
The steroid jabs have many long term problems - but my vet said that if it improved his quality of life NOW it was worth the risk.
F.A.B. is an excellent site.
http://www.fabcats.org/owners/disease.php and Petethevet on facebook can give good advice.
It is such a worry. Frankie sounds awful when he is coughing.
Good luck