Is it ok to conceive a child while sick? (no fever) could it hurt the baby?

Probably ok. It is not a good idea to plan to conceive a baby if one is under the care of a physician for a serious illness. On the other hand , most women have several mild illnesses during the course of their pregnancies without adverse outcomes to the developing infant, although regular prenatal care is essential to having a healthy pregnancy and infant.
Usually. Conception is really a drawn out process more than a single event. The egg is released and must reach a point in your tube where fertilization is possible. Fertile sperm must join up with the egg within a set timeframe, then the product of that union must travel to and insert into a prepared womb. The process takes a week or more, so your day of discomfort is unlikely to matter.