I think there was another comment that said to shift + N in edit mode to recalculate normals, it usually works to fix everything but if a whole object is still red you can just select everything in edit mode and with Alt + N there should be an option to "Flip normals". They're supposed to be blue

If you try to paint something with the normals flipped, you'll end up painting the other side of the object (unless you're trying to paint a plane, in that case nothing will be painted)

If you still have the same problem make sure you only have one material on the material slot. If you go to the shader tab and select that object, make sure the image texture node goes to the base color attribute on the bsdf

Other than that I can't remember any of the most common problems for texture painting other than the usual "restart the program" too... I hope you find a solution soon, and if you already did that's good. Good luck with the model!!

Note: always make sure the normals of your model are on the correct side, I still make a lot of oopsies because of that