Firstly, I'm a hoof care practitioner & my opinion is very much along the 'natural' lines(tho the 'natural' lable grates, can't think of better). I also do not buy that shoes are necessarily 'evil' either. I am not adverse to horses being shod, assuming of course it is well done, the horse is well managed, etc, etc.
However I do think they are *generally*(there are exceptions) unhelpful & often detrimental to unhealthy feet. I do believe that shoes only mask problems(can elaborate on why later if you like). Just because this horse may have walked out OK with shoes & was only 'lame' when deshod, doesn't mean the shoes were helping her, except in a palliative fashion. In fact, especially as she seems to have such serious probs & is still only a baby, IME effectively 'ignoring' the issue by masking it with shoes, I would expect her to be chronically lame even with shoes before long.
Therefore I would personally advise that it is better to keep a horse in this condition unshod. *That is not to say she should necessarily be left barefoot tho*. So in answer to your question, I would wait until her feet are healthy & strong before considering putting shoes on her. There are other, generally appropriate & far better methods of protecting feet when necessary these days.
Some hoof pics would be helpful, to get a better idea of the state of her feet & what may be required. Also info on diet & management. Diet is one of the single biggest factors in hoof health, and unfortunately, intensively kept & fed equine athletes generally have pretty unhealthy diet & feed regimes. Eg. Starchy or sugary feeds are generally bad for horses, and laminitis is one regular problem that this sort of diet causes(through something called 'hind gut acidosis' and also insulin resistance). Large, infrequent meals also add to the problems, for horses designed to be 'trickle feeders'.
So, without further info, of course I don't know, but from experience, I imagine that diet, management and being shod at such a young age are the big parts to her problem. I imagine she's a 'typical' flat footed, weak heeled TB? If she is so sore just in your soft paddock, then it would seem she has quite serious problems and I would advise not leaving her bare, but using boots, pads, Vettec SoleGuard or such, to provide the protection & support she needs to the bottom of her feet. It is not usual for a horse, even with severely compromised feet to require 24/7 protection/support for too long tho, so long as they get the right care. It is usually a matter of weeks before a horse will be comfortable at least in their paddock. It will depend on many factors tho as to whether she may continue to need boots or such for work, or for certain situations.