Shields count as direct, yes - they may not allow the milk to be removed as easily, that's why they have their drawbacks.
It's not 'evil' to give formula - as if
But you need proper help and the chance to discuss everything sister - you have been feeling low and pressured for 6 weeks, and as far as I can see, no one has really met your needs. This isn't a feeding 'problem' or at least not solely a feeding problem - is your HV any good? Can you talk to her about your options?
Right from the beginning when your midwife suggested formula on day 2 and day 5 when you were solely expressing and feeding by syringe....you have had enormous challenges and (as far as I can tell) not very good professional help. All this has made things worse, and my heart goes out to you.
Sticking with one person/source of information you trust and can respond to will help, someone who really listens to you, and helps empower you to make up your own mind - that might be your HV, it might be the counsellor, it might be a knowledgable friend....but it has to be someone who can see you, IMO.
I hope things go better for you.