You can arrange your own investments and you don't need advice. you can buy advice on a fixed fee basis and then make the arrangements yourself. Yes if you want somone to manage your investments, they will charge you for doing it, just as if you want someone to clean your house, they will charge you for doing it. Social services REALLY can't give you advice about managing your finances. Get advice HAS to be their stock answer, same as it had to be mine when I worked in the NHS I mean this politely but its a gamble. if the annuity will pay your fees for the rest of your life, (it would need to be a honking annuity!) then you are sure to be able to stay where you choose. if you sell the house and invest the money, unless is a huge house in a high value area, that will slow the trickle of money but I am betting you won't be able to avoid eating into your capital whether or not you invest yourself or employ a manager.
I am so sorry, you don't need the added stress and neither does your daughter. I think really if it was me I would be deciding what is the most important thing to me....staying in the place I chose but knowing the money would die with me or maybe leaving money behind but risking having to move care home.....but either way are you SURE that your choice will fund your care?