It looks like it is in great shape, coming to the end of its blooming cycle although good light, not strong direct light, could extend that. Keep touching the soil to make sure it feels damp but not soggy. The paper could be removed , it is purely decoration and might impede drainage a bit. I think this is one of the Rieger begonias, you could look up more about the on line,

Hi Rachael, I'm very sorry to hear about the loss of your cousin. She certainly loved a pretty flower. Just wanted to say that this is a beautiful begonia. I'm sure you'll enjoy it for a long time.

i keep my riegers indoors in partial sunlight, either by the eastern or western windows - for sev hours of very early or very late sun. they rebloom for me too. i slowly trim the longest 'flower stems' and pinch at the top to encourage branching - which in turn will produce more flower shoots.
it needs to be slightly moist, don't allow it to dry out more then 1-2" from the top. mine are on self-watering wicks in shallow azalea pots.
when it stops producing flowers, trim the top growth and start keeping it much drier (but never totally dry) for may be 3-4 weeks, until you see new growth at the bottom. then you can cut off more ratty old leaves. but not too soon. when i trimmed them down to 6" like it was recommended they did not have enough leaves to produce secondary growth and they died.
so now i remove older leaves slowly 1-2 at a time, while the new ones are emerging. and it worked.
it will take sev months for it to leaf out to full size and then it will bloom again in the fall.
once it's growing well - you can pot up to next size pot (2" larger in diameter). i read that they don't like to be pot bound.
mine got quite large in a bigger pot (it was a reg 6" starter plant like yours).
i grow them in half african violet mix half perlite (and on wicks like AVs). AND i feed them continuously like AV's with 7-7-7 (i double the dosage) fertilizer in water.
or you can give them time release osmocote 14-14-14.
and even 15-30-15 for more blooms once they are bigger and growing strong.
my 1st plant was your size in may and it did not get much larger until it got a larger pot.
here's what it looked like in nov the same year, just beginning to rebloom.

oh, i forgot to mention - it's a very thirsty plant! since mine is on wicks i can tell you it sucks up 1qt a week when it gets big. just so you know to watch it carefully.
and if it's not producing enough flowers when in bloom - that means you need to give it more light.
it is also a short-day plant like holiday cactus and poinsettia. it needs shorter days to initiate blooms, but once flowering...it does not matter, it'll keep going.
so basically for twice a year blooming you need to catch short days in early spring and then short days in fall.
mine starts budding in march and goes thru june. and then buds in oct again.

Speaking of Riegers, a large local nursery had a big plant sale table last month and I spotted two Riegers in six inch pots, looking good, although one was obviously rotting at its base. They were two for $7 so I bought one good and the rotting one, thinking it might be interesting to prop the bad one as so much of it was firm and healthy. To my surprise when I took the bad one out of the pot there were no roots in one of those tight sphagnum mixes, only a two inch black net pot holding what appeared to be a rotting marble-sized tuber, also in tight sphagnum. I can't imagine why the roots would disappear, it must have had them once, and usually they would be in the pot ,black and dead looking. I was ab le to prop several pieces although it will be fall, I guess, before I will have a sizey plant,

commercially they usually take cuttings from last year's sprouting canes and root them. at least one node should be buried in mix: half peat half perlite is good, bag it too. or just a starter mix is ok.
so you can do that for 2nd plant 'rotting at the bottom'.
i haven't poked around in my 2nd yr's plants pots, but i thought reigers don't have tubers, they are fibrous type.
so may be yours are not reigers? or may be it was just a swelling of the stem, not tuber? like a codex?
then i thought about solenia. it is also a hiemalis type, i searched for that one too - even unearthed a patent for it. and it states that there is no tuber.
but non-stops and go-gos look very similar to it, but will develop tubers if grown long enough and at lower temps in the fall (mine did!). pic?