Thanks for your question on Health Care Magic.
I can understand your situation and problem.
You are having blunt
chest trauma due to fall in Bath tub.
By your history and description, possibility of musculoskeletal injury is more. And the things you are seeing, slight
tanning,
redness, veins etc are due to
inflammatory edema because of musculoskeletal injury.
So no need to worry much for heart damage.
Better to start painkiller, anti inflammatory and
muscle relaxant drugs.
Apply warm water pad on affected areas.
Avoid heavyweight lifting and strenuous exercise. Avoid movements causing pain.
Don't worry, you will be alright in 1-2 weeks.
If not improving after 1-2 weeks or worsening than get done chest x ray to rule out internal damage.
Hope I have solved your query.
Wish you good health. Thanks.