Welcome to HCM
We understand your concerns
Your doubts about the semen is definitely baseless. For any organic life form it needs favorable conditions to stay alive. Bathroom / toilet condition are not so suitable for them and semen may not stay alive for more than 15 minutes.
Secondly, Semen does not have the capacity to climb up through somebody's vagina and enter uterus
and create an egg. The female members of your family will never be affected.
Don't worry. Be happy.