I'm looking for a pretty red, white or pink flowered plant that grows no taller than 18" and is non invasive. Everything I come across seems to be at least somewhat invasive...any suggestions would be great.
What do you mean by invasive? Spreading? or something that seeds all over out of the area?
If you never ever want to have to pull something out or cut it back....you better be thinking annuals....but you will have to plant them every year....unless you get something that freely reseeds and then it could be considered invasive.
If you are looking for a plant that is pretty, low growing and that you never ever have to do anything to....best be thinking plastic plants.
I like lamium for a pretty low growing plant....I do have to pull some of it out when it spreads further than I would like....but it blooms white and pink and has nice varigated leaves and comes back every year so I don't have to replant.
I'd agree that with your restrictions, annuals may be the best way to go. Most perennials will achieve heights in excess of 18" with maturity, but very few of them are what I'd consider invasive or aggressive spreaders or reseeders. You might want to consider sedums or stonecrops - tough, hardy and drought tolerant plants. Low growing carpeting ones DO spread but very manageably. Upright ones may get taller than you wish but height can be controlled by pinching back in early season.
What season do you want the bloom? Aster 'Alert' is small and blooms red in late summer. 'Pardon Me' Daylilly has red (not cherry red) blooms and will bloom sporadically through the summer. 'Veronica Red Fox' is about 18" and has a fairly long bloom if deadheaded.
Dianthus is nice.
Moss rose (portulaca), impatiens, petunias, marigolds. There are also low-growing zinnias.
I always do my borders in alyssum and lobelia. Alyssum does reseed itself rather profusely, but it has a shallow root system and is easy to weed. Lobelia will fry in the heat of VA but it comes in blue, red, and pink (maybe more colors). They are both less than 6" tall.
Depending on the scale, miniature roses or carpet roses are small, colorful, and bloom prolifically in a variety of colors.
ajuga, forget-me-nots, shorter versions of shasta daisies(Snow lady or Silver Princess variety)Marigolds, verbena,creeping phlox, california poppies, portulaca, short daylily. What about dusty miller? Even Ice plant, verbena. What about some of the mini daffs?