First I will advise you not to panic, rather face the situation with patience. This is a case of laryngo/ hypopharyngeal cancer with metastatic neck node... You didn't mention about the status of the lymphnodes in details. Anyway till now what information you have provided this is a case of Stage 3 cancer if the node is not fixed or less than 6 cm in size and in that case this is obviously in curative stage. But in case of fixed node or larger size( more than 6 cm)it would be stage 4, still can be treated in curative intent.The lung changes don't seem to be hematogenous spread from hypopharyngeal cancer. Coming to your another question regarding the role of PET- CT, you need to know that it would be most preferred if you can afford PET- CT, but in absence of Pet ct you can do CECT thorax to rule out lung metastasis which you have done already I think ( as suggested from lung findings). Lastly I would suggest that,  have faith in your doctors and the tumor board,  as there will be a consolidated opinion from all the specialities and experts and they will definitely guide you what is best for the patient.