A red image pops up when I take a pic

Hi,

I have an DMC-FZ7K, I know exactly what you mean.

The red box with the arrow inside it flashes because the camera is writing the pictures or videos to the SD card.

When you stop taking a video, the box disappears, because the video has finished transferring to the card.

This red box is perfectly normal, and nothing to worry about. Furthermore this has absolutely nothing to do with the battery being dead or the card being full.
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When the battery dies, only the BATTERY ICON flashes.

When the SD card is full, a message saying so pops up on the screen.
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Here is a link for if you would like to recover the pictures you deleted:

I chose the DMC-TZ3A since I didn't know what the letter was at the end of the model number for your particular camera. If this is the camera

Here is a link to the manual

If not

Here is link to the Lumix series cameras

Pg 25 indicates that flashing red in the upper right corner is the battery needing to be recharged. If the battery was recently recharge and its turning red on the screen, it could be that the battery isn't holding a charge and may need to be replaced.

I didn't see any other error messages on the screen indicating that icon unless b,c, or d models have a different error message in that area of the screen.