Crepe myrtles will sucker badly after they reach a certain age-around three, lol, like yours are:) Tree or shrub varieties both seem to get an urge to spread themselves after they've been in the ground a few years.
So you will need to decide how you want the mature plant to look and begin a regular pruning programme that will continue as long as it is in your landscape.
Is yours a tree variety? Do you want a central leader? Then you will have to be diligent about pruning out everything but the one central 'trunk'. If you want the more traditional three leaders, then choose the three straightest growing far enough apart that none will rub against the others as time passes.
Is it a shrub variety? Lol, you may have to do some research to be sure, but I have seen shrubs pruned to a tree shape with one-three 'central leaders', and while it takes a bit more work (shrubs like to sucker profusely), it can be worth it if you wanted a tree and accidentally bought a shrub. The shrub won't grow as tall as a tree variety will, but that may suit your landscape better anyway.
It's really not that hard to prune crepe myrtles in a way that makes them an interesting landscape feature practically year-round, the bare winter crepe myrtle is truly lovely as a sort of living garden sculpture and can be lit over the holidays, or spotlighted for an elegant and dramatic focal point at night.
Also, going forward you will have to routinely prune off those dead ends-as soon as the flowers brown off or fade (your clue is the blossoms aren't pretty anymore), cut the 'ugly' out off. Similar to deadheading a flowering shrub or annual, doing so means you will enjoy at least one more flowering in that season. I managed as many as three flowerings with our south AL and central FL crepe myrtles but even when I lived in NW GA I was able to get two flowerings from my crepe myrtles.
At this link Georgia's best loved gardener, Walter Reeves, tells you all about pruning this lovely plant properly:
The page has several links to more information on caring for the crepe myrtle in the home landscape.
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