Hello and welcome, I am Dr. B and would like to help you today.
Now this is a bit of an odd situation. Chlamydia does require a long course of antibiotics ( doxycycline for at least four weeks) but is very curable. So you need to have a serious conversation with his vet about using a long course to clear this. Or you need to consider a second opinion from an alternative practice. If you go for the later, it's advisable to make sure nothing else is causing his signs ( ie herpes virus) and that nothing is perhaps compromising his immune system this preventing him from clearing this ( ie fiv, felv). These are quite important since again Chlamydia can be cured as long as all cats in the house as treated ( to prevent carriers as well as help the affected cat).
Otherwise, steam treatment ( using shower steam), saline nasal drops, and saline eye flushes can help reduce the signs and keep him more comfortable. But again if he is has relapses then we need to review their treatment or make sure there isn't something more they have missed.
Please take care,Dr. B------------------------------------If you have any questions, don't hesitate to ask. Afterwards, please make sure to rate my help ( using the stars or typing a rating) as this is the only way I am credited for helping you. Thank you. :)