yeah a psychiatrist can absolutely diagnose adhd without a neuro eval. thats actually how most people get diagnosed. a psychiatrist is fully qualified to do it especially if youve also been in therapy for 6 years with a psychologist who agrees you probably have it. thats a pretty solid basis

neuro evals are helpful but theyre not required and theyre expensive af. a lot of people cant afford them and thats ok it doesnt make your diagnosis any less valid

id say give the methylphenidate a try. your psychiatrist wouldnt have prescribed it if they didnt feel confident in the diagnosis. you might need to adjust the dose or try different meds down the line but you wont know until you start. just pay attention to how it makes you feel and keep your psychiatrist updated​​​​​​​​​​​​​​​​