Hi Welcome to HEALTHCARE MAGIC..
I have gone through your query and can understand your concern...
As per life span of sperm after ejaculation it depends upon a number of factors, the most important of which is where the sperm are located. On dry surface as clothing, skin they are dead as soon as semen in dried. However in wet surfaces like vaginal or
uterus mucosa they could live for maximum of 3-4 days depending upon the quality of semen. However vaginal secretion does not kill the sperm, of course this environment is best suited for them.
As per
pregnancy possibility in you. Yes, you might get pregnant with intercourse approximately a month after having given birth to a child through c-section. However chances of pregnancy as less until you have started regular
menstruation & during
lactation. Pregnancy is also not advised just after a C section. You should avoid
unprotected intercourse in future.
You should also do a pregnancy test to rule-out pregnancy possibility.
Refer to a gynaecologist, if problem persist
Hope this information helps