Sounds like a few separate issues we need to isolate to deal with.
What happened to make her afraid?
Can you recall anything in the lead up to her becoming terrified of you?
I would not give her a day old duckling, chances are she would kill it or ignore it at best. The chances of her adopting it are slim even if she was happy and stable, which she is not right now --- to introduce it now would most probably be fatal.
If she's not broody, there are a few things you can try to assist her in that direction, but generally you can't make her, and her being broody won't make her accept a baby that isn't hers.
If she's terrified to the point of trying to harm herself to get away from you, trying to breed her is a bad idea. Our physiological state impacts what genes are turned on and off, the same is true for animals as well. If you breed her in a distressed state of mind, especially a prolonged one, it can have a severe impact on the offspring who can actually inherit that state or show heightened levels of aggression as a response to the circumstances they were conceived in. She will make a terrible mother if terrified, you'd be unlikely to keep any offspring for long, even if you could get her to be a mother which isn't likely in this state. If she is terrified because of a mental imbalance, the male may attack her rather than breed. Insanity distresses animals because insanity is unpredictable and illogical, and their normal body language etc will not be received correctly which means they are at risk of attack from the strange-acting one, which provokes some animals to try to kill the abnormal one.
Is she terrified in general, or just of you?
Have you started taking any medication lately?
I don't know if that's an acceptable question on this forum, if not then apologies, but bear in mind that some medications can make you smell very different or appear different to them and this can scare animals.
Sometimes toxicity, or poisoning, can cause anxiety and outright terror because their neurological system is overwrought and they are unable to calm down and stop overreacting to everything. More calcium can help with nervous hysteria.
I don't know what is used to get rid of lice in ducks, I use gentle natural things in the diet or topically, but an advanced case of lice may be best treated with harsher things as it can kill rapidly. There are natural and harsh things to use but I won't be advising a newbie to herbs to use such things.
I've read with chooks that when they're laying a clutch you can use the aluminium foil method to encourage broodiness, something I expect I'd never do but each to their own... However if your duck is not laying a clutch you can't encourage it. You could start tampering with lighting to change her hormonal seasonal cycle but I can't advise you there either as I don't do it. Either way, with the state she is in, now is not the time to think of breeding her. It would be a disaster.
You should deal with the lice first and the fear second and maybe months down the track she will be in a fit state to breed. The duckling's life is probably forfeit if you put it in with her.
Best wishes.
