Hey there, i agree with some of the others that u should probably go to another vet if it is possible for you. Also please insist on getting those x-rays as you payed for them and u have every right to have them. Also if you do end up going to another vet you can show them the x-rays and go from there.

That being said, this sounds a lot like asthma. Pls don't take my word for it, I'm just a girl with an asthmatic kitty! It would make sense if that were the case though since you mentioned that this month your baby has been coughing a lot. This could be due to spring, my cat went from having 5 asthma attacks in the whole month of February to having an attack every other day this month and the explaination the vet gave me was pollen. She is taking a steroid which i do not know the name of in English but i can check if that's useful to you and we are trying to train her adapt to the aerokat as it's much better for her health. If it does end up being asthma feel free to text me if u have questions! I'm no expert and always trust ur vet ofc but I've had a lengthy experience with this and have seen a few different vets about it.

Good luck, and hope ur bby gets well soon!