With a new image ready to apply textures to, use Blender's Texture Paint mode to quickly brush texture colors onto your mesh:
Navigate to Texture Paint mode.
In the viewport, select your t-shirt mesh, then open the sidebar tools to access brush settings.
Select a color, brush size, and falloff. You might need to adjust settings, depending on the modifications you intend to apply.
Draw on either the UV 2D map or the 3D mesh.
Save the .png of your texture map by selecting Image > Save.
You've completed the texturing section of this tutorial. If desired, download a reference sample of this project and texture image for comparison.
There are a lot of ways to texture and apply a unique appearance to your meshes. For additional suggestions, try utilizing alpha transparencies, unique seams, PBR textures, or Blender's other texturing tools and techniques.