Which eyes Arya closed

Has Nymeria been following Arya all along?

No.

It's not on the show, but in the books, Arya has a couple of warg dreams where she looks through Nymeria's eyes and essentially roams the Riverlands forests.

Out a storm of swords II: blood and gold (Chapter 65, Arya XII ):

When they are in the Foothills of the mountains of the moon found the rain had mostly stopped. Arya could see the sun, moon, and stars, and it seemed to her that they would go east . "Where are we going?" she asked again.

This time the dog answered her. "You have an aunt Eyrie . Maybe she wants to get rid of your skinny ass, even though the gods know why. Once we have found the main street, we can follow it to the Bloody Gate.

As shown in this quote, by this point Arya and the dog have left the Riverlands behind and are moving towards the Arryn Valley. At this time, Arya has a very vivid dream:

That night she went to sleep, thinking of her mother and wondering whether she should kill the dog in her sleep and save Lady Catelyn herself. When she closed her eyes, she saw her mother's face on the back of her eyelids. It's so close I could almost smell it ...

... and then could you you smell. The smell was faint under the other smells, under moss and mud and water and the stench of rotten reeds and rotting men. She paddled slowly through the soft ground to the River bank , had a drink, then raised his head to sniff. The sky was gray and thick with clouds the river green and full of floating things. Dead men clogged the shallows, some still moving as the water pushed them, others washed up on the banks. Her brothers and sisters swarmed around her, tearing at the ripe flesh.

Although not identified by name, the river mentioned there is believed to be the Greenfork (the river near the twins), far back in the Riverlands.

Out a dance with dragons II: After the party (Chapter 45, The blind girl ):

She opened her eyes and stared blindly at the black that covered them. Her dream was already fading. So beautiful. She licked her lips and remembered. The bleating of the sheep, the terror in the shepherd's eyes, the noises the dogs made when she killed them one by one, the growling of their pack. Game had become scarcer since the snow began to fall, but they had eaten last night. Lamb and dog and mutton and the flesh of man. Some of her little gray cousins ​​were afraid of men, even dead, but not of her. Meat was meat and men were prey. She was the night wolf.

But only when she was dreaming.

It's even more obvious here. Nymeria is still back in Westeros (where winter falls) and while the exact region is never identified, it is certainly nowhere near Arya, which at the time is in Braavos is .

There are also multiple mentions of a giant wolf pack terrorizing the Riverlands.

Out a crow festival (Chapter 44, Jaime VII ):

The next day, Ser Dermot returned from the rainforest to the castle empty-handed. When asked what he had found, he replied, "Wolves. Hundreds of bloody beggars." He had lost two guards to her. The wolves had come out of the dark to devastate them. "Armed men in mail and boiled leather, and yet the beasts were not afraid of them. Before he died, Jate said the pack was led by a she-wolf of monstrous size. A direwolf, to hear him say. [. ..]

"A ring of fire around your camp might keep them away," said Jaime, although he wondered. Could Ser Dermot's wolf be the same animal that Joffrey had met near the intersection?

This time the area is clearly marked: Jaime is in Riverrun at this point. Arya has since left Westeros and has already spent some time in Braavos.

It seems like Nymeria pretty much stayed in the area Arya puts her in The Game of Thrones left behind and made it the territory of their pack. This is where Arya also meets the pack mentioned in your quote and meets Nymeria in Season 7.