Are there houseplants that flower inside? We have a fair amount of light.
Indeed, there are many flowering houseplants, such as African Violets, Begonias, Hibiscus, Flowering Maple, Oxalis, Peace Lily, Anthurium, Christmas Cactus, Gloxinia, Geraniums, and more! Your local garden centre will have several varieties from which to choose.
For some information on houseplants in general, take a look at our Beginners Guide to Growing Houseplants.
And for more detailed information on growing African Violets and their relatives, see the Guide Growing Gesneriads.