I don't think you're at any special risk of having a baby with health problems, unless there are problems in the family.
As for the bleeding thing when you were younger- it's not unusual for baby girls to have a weird kind of period when they are newborns, it's caused by hormones the mother produces during birth.- how old were you when that happened? If it was right after you were born, it could have been that- I think it can even happen later on, if you are still being breastfed, and your mother produced seem extra hormones for whatever reason.
I wouldn't give it a second thought if I were you, not untill you've been having unprotected sex for a good few months without success- where I live, they won't ususally investigate infertillity until a couple have been trying for 2 years.
Good luck, but most of all, enjoy trying !!!!!