Hi Willows . . .
First I have to say that your best chance to keep your rose, and enjoy it for many years, is to pot it up to a larger container -- take it OUTSIDE -- and eventually plant it in the ground.
The problem is that these little roses are grown up to be used like a bouquet of cut flowers -- kept until the blooms fade, and discarded. YOU DON'T HAVE TO DO THAT! But you DO have to treat your little plant as a rose.
So, you need to know that this little plant has been kept dwarfed, and pushed to bloom all over, and it's going to take time to recover from that. And it does need to be in a bigger pot.
Roses, sadly, aren't indoor plants. They're not "houseplants." In fact your little guy could grow up to be anywhere from 2-ft. tall to 4-ft. tall. And he could please you with blooms for many years.