Oh dear, the last hairdresser you went to doesn’t sound very experienced as you’d never use a 5 as a lowlight against very light blonde hair. That’s just bonkers thinking and was obviously going to look awful. Head and shoulders will just dry your hair out and cause more damage. It isn’t a proper colour remover so please stop using it, as it isn’t helping your situation. Focus on adding moisture to your hair at this stage.
You need to find a hairdresser/colourist who is an expert with colour correction and ask for a consultation so they can look and feel your hair and offer you some options. Try a few salons/hairdressers before booking in. Hopefully, it will become clear by what they say, whether they are knowledgable or not.
I think at this stage, if you want pretty hair, assume you won’t find a budget solution as your hair will need careful handling as it’s likely to be quite porous and take colour unevenly so will need an experienced colourist to deal with that.