I'm not sure I can help with your plant's health, but I'm pretty sure it's a Graphophyllum pictum, a "cariacture plant" of which there are several colour variations. If you google for those names you may find information to help save yours.

Here is a link that might be useful: cariacture plant

once you have the ID.. most of us would consider it a houseplant.. or maybe even a tropical ... learn more in those forums ...

what did you fill the pot with .. looks almost like sand ...

and is there any drainage in that pot????

on some level.. its probably transplant shock ... and moving it to sun.. was probably not wise ... to confirm such.. is it old lower leaves that are worse off .... compare with the growth points ... if they are looking OK ... then it is shock ...

perfect watering ... and you should be all set ...

ken

Looks a lot like a Pseuderanthemum atropurpureum "Tricolor" or other similar tropical shrub sold as a houseplant - I see them all the time in the grocery store and places like Home Depot and have owned several over the years both at home and in the office.

Moving it to the balcony was smart - it needs at least partial if not full sun. The only way to keep it healthy indoors is in a very bright window or with a grow light unless you are fortunate to have a balcony. It needs rich soil, well drained, and to be fed regularly and watered generously. Give it some food and water and it should perk up. Can't tell for sure from the photo but it could probably stand being moved to a larger pot. I've usually fed these with dilute azalea food alternating with dilute houseplant food although palm food would work as well - it likes acidic soil. It doesn't like to be in mud but don't let it dry out completely either.

These plants are prone to spider mites and scale indoors if they are neglected or not watered enough - the insects tend to attack struggling plants like this one. My usual way to deal with this is to spray with a solution of water with some canola and a bit of clear soap (like 7th Generation or clear Joy or Palmolive).

If you see hints of anything suggesting insects (small spider webs for example), take it out into the driveway and give it a brisk spray with a hose first and then spray with soap and oil solution.

If it likes its location and it's well cared for, and can get 4 feet tall or taller. I had one get to nearly 5 feet in front of a floor to ceiling window in an office..... that thing just loved that spot. You do need to rotate the pot every few weeks though if growing in a window,

Moving it to the balcony was smart

==>>> with the caveat of shocking it.. if you dont properly harden it off to an extreme change in sun intensity ...

ken

I've never "hardened" off a plant to a change (even an extreme one) in sun intensity. Actually, I've never heard of doing that. I've spent most of my life in the Northeast where hardening off is what we do to seedlings that we start indoors to get them used to cool springtime outdoor temperatures.

I wouldn't put most of my plants -- even the sun-loving perennials -- into bright, unrelenting sun without any protection. They would simply fry. But your point (if I'm getting it correctly), is that even in bright sun, it may still need a bit of shade or protection from too much sun. We found that not just on our deck but in our garden as well and actually planted some trees in our sun perennial beds.