The TARDIS has finally been able to convince the Doctor to take a stroll outside, see the sights of the planet she's taken him to, maybe get into some trouble. The loss of the Ponds in Manhattan has made him glum and solitary; he's been holed up in her innards and her libraries for weeks now, and as much as she loves the attention, it worries her. She can see the grief and desolation plainly in his mind, so having him engage with the outside universe again gives her hope that he may be starting to heal.
She's entertaining herself by scanning local transmissions for anything interesting, when all her senses are suddenly and violently assaulted as she is being dragged through space, time, and the very walls of the universe. After a nanosecond of utter shock, she fights against the unknown force, engines roiling and Cloister Bell ringing. But there is no one to hear it.
The cool air of a New York morning is fiercely torn open by the Rift spitting out a large blue box, which is wheezing and groaning painfully. The TARDIS is struggling to control her flight/fall, and she shoots across a lake, just barely clears a small bridge, and mows over a trash can before being harshly stopped by a group of trees. Fortunately it is rather early in the morning, so with some luck nobody saw her undignified landing.
Not that she's concerned with that at all. No, there are too many more important things going on all at once - with terror she realizes that she's in a different universe, one not connected to her own, which means there is no vitally important energy she can draw from it to survive; it's like drowning, or having all the oxygen sucked from her lungs. But at the last moment she manages to cling to the Rift like a lifeline; long ago the Doctor modified her to be able to process rift energy and here at its center it's strong enough to keep her systems powered, to keep her alive.
However, there is no time for relief; as soon as she stabilizes somewhat she tries to push back into the Rift, even though that is objectively a very bad idea. She's clinging to the vain hope that it might still be connected to her home universe, that she could follow her own time trail back through it. She phases in and out of reality with increasingly labored groans of her ancient engines, the fabric of this world straining under the strength of her desperation. But the opposing forces within the Rift are too strong even for her and after some time she shudders into existence with a final thunk, engines simply giving out, drained of all energy.
She's trapped. She's trapped in a universe she can't live in, without the Doctor. The anguish of that realization is more overwhelming even than her near perishing just now. She might as well have died, it would have been kinder than this. Though for all that, she doesn't feel quite as deserted and incomplete as she would have expected. Could it be...
Cautiously hopeful despite her misery and exhaustion, she extends her senses and actually gives her surroundings a cursory examination, absently noting that she ended up on a parallel Earth, again. And... yes, there he is, within the city boundaries even. He isn't quite hers, she can tell, and that aches deeply, but still so much less than the alternative would. Did he notice her arrival? Is he going to come find her? There's an easy way to answer those questions.
...If she was native to this universe and its Time. With resurging panic she realizes she can't see, can't view the intricately winding paths of decisions and actions, of events and consequences and probabilities. It's all wrong to her, all shunted at the wrong angle, grating against her perception subtly but irritatingly, just barely obscured as though through a veil. She may as well be just any blundering, blind actor in the merciless grasp of Time, here. Only the fact that she's not entirely unfamiliar with this feeling - she's been to universes without Time before - keeps her from balking and panicking outright. She is also similarly limited whenever she uses her humanoid form to interact with people, simply because it's impossible for her to perceive reality both as an agent within events and as an outside observer at the same time. But still, the prospect of being caged in this plane, unseeing and linear, is distressing.
Instead of dwelling on that, she focuses on the Doctor's presence again and decides to draw his attention somehow, both for her own comfort and because together they will surely be able to find a way back through the Rift. At length it occurs to her that without her knowledge of events, she is free to act and interfere with this world - far from a fair trade-off, but not entirely useless. Checking the outside for dangers and conditions, she slips into her physical body and puts on a thick woolly dress, tall shoes, and a scarf (she's had some bad experiences with the cold before). Trying to focus on the task of physically locating the Doctor instead of getting overwhelmed by everything she just went through, she steps out of her shell to explore.
TL;DR: shit sux big time