Maybe you look less like Sunshine’s original human companion in the cold like of morning? Also, pay attention to what colors you’re wearing…some birds react badly to certain changes in appearance. Put the shirt you wore yesterday back on and see if that helps.
Overall, however…
Slow and steady wins the birdie heart. Parrots have a natural flocking instinct – they want, nay, need to have social interaction with peers – and they’re capable of recognizing us as their intellectual equals. Sunshine wants a flock and will accept you if you win her trust and establish your qualifications as bird-like.
But it’s a trust-winning exercise, first and foremost. Don’t force her out of the cage, and don’t force your hand in; to add to the difficulty, lovies and females in general (and just for the record, it’s not yet clear that Sunshine is a female, but I’ll use “she” for convenience) are somewhat more protective of their cages than other parrots and males.
Instead, within her sight, do quiet, relaxed activities, including eating and a lot of things that do not involve looking directly at her. Let her observe you being non-predatory, non-threatening. This will take time – maybe lots of it, I once spent about 5 months winning the trust of a rescued cockatiel, and we never did win the love of 2 of our female budgies – but it’s really the only way; you can’t force it. Sunshine is VERY early in this process, but the loving last night shows promise. Talk quietly in the background, be present in her life, be in view. It helps to read or watch TV or whatnot to keep yourself from getting bored or succumbing to the urge to rush things, and let her set the pace. Approach slowly but not like you’re stalking prey; look at her sideway out of one eye, then look away as if shy – a lot of folks have success playing sight games, moving into and out of the bird’s vision, looking at and away, and otherwise flirting like a strange bird introducing itself to the flock.
Meanwhile you can be reading about lovebirds from the library and the Internet. 
Lovies sure can nip with those proportionally laerge beaks! If you need to change food and water without getting bitten, you can use one hand holding a colorful piece of cloth or toy as a distraction on one side of the cage while the other darts in to change the dishes.
A little incidental nipping is part and parcel of parront-hood. Do not react to it; parrots love drama (look up “the drama reward” on parrot info sites) and will interpret even being yelled at as attention and reward. NEVER blow, tap, flick, or hit, of course. The less you react to a nip the better.
Birds don’t understand punishment or discipline. Eventually (once you’re accepted as a flock member) you can use “laddering” to curb nipping, but you can’t use it yet. Laddering consists of stepping the bird up from one hand to the other (hence like a ladder) just rapidly enough that the bird has to pay attention to footwork and forget the biting; it operates off the principles “Interrupt, Reinforce, Praise, Distract.” Interrupt the bird’s conecentration on biting, best by introducing a colorful toy into view with the othe rhand, or just by bringing the other hand over and stepping her up; reinforce an ingrained habit of obedience (birds are not very obedient, but stepping up when a finger is placed at their belly is a very natural reaction and constantly used, so the bird is very likely to do it, making it a good choice for the reinforcement phase), praise the bird after she’s done just enough “rungs” on the ladder that she’s stepping up consistently without biting or fussing; immediately distract with a new toy, activity, or perch…basically something interesting.
The goal of laddering is to replace the bird’s frustration with the “hey I just did the right thing and got praised for it” feeling and the biting activity with “ooh shiny new thing.” The distraction is a reward, but it does not follow biting, but instead follows a proper behavior you want to encourage (stepping up).
The universal advice for people with a brand-new parrot which has not accepted them – take it slow for now! Patience is your weapon to defang that beak.
Best of luck to you; keep us updated.
Sailboat