A drain backs up when it rains because water that belongs in the storm system is getting into your sewer line. Most DFW cities run separate storm and sanitary sewers, so rain should never reach it. When it does, the usual routes are a cracked or root-damaged private line, a downspout tied into the sewer, or a missing cleanout cap.
Utilities call this infiltration and inflow. Infiltration is groundwater seeping through cracks, offset joints and root holes once the soil around the pipe is soaked. Inflow is surface water pouring in through an opening: a roof downspout or yard drain someone connected to the cleanout, or a cleanout with a broken or missing cap. The EPA lists sewer defects that let in stormwater and groundwater among the causes of sewage backing up into homes.
The lowest drains show it first: a ground-floor shower, tub or floor drain, then the lowest toilet. A line that drains normally in dry weather, backs up in a storm and clears once the rain stops points to water getting in, not a clog. Walk outside and check that the sewer cleanout is capped and that no downspout pipe runs into it. A sewer camera inspection shows cracks, offset joints and roots, and where each one sits.
One honest limit: if neighbors back up in the same storm, the city main may be overfilled, and no repair to your own line stops that. Only the city’s work, or a backwater valve on a home that sits low enough to need one, keeps that water out. Most DFW slab homes do not, so report a street-wide backup to your city’s water utility first.