33 weeks tomorrow and I may have to have a C section

Emily • First time mama!
Feeling kind of worried because our baby is measuring big (5 lbs 6 ounces). I do not have GD. My husband is tall and has big babies in his family, my doctor said there was a chance I may need to do a C section.
She will check at 36 weeks to see how big he is again. Right now my plan is to try to give birth vaginally, and if unable to, have a c section (worst case scenario). No my doctor is not trying to push me into one...she just said there was a chance because of how big he might be and the risk of him having nerve damage when going through the birth canal etc. she also said there was 15% error margin with guesstimating the baby's weight. I just wanted to share my concerns on here. I am worried about having 3rd or 4th degree tearing from the baby if I deliver vaginally. I know there are a lot of woman who are against c sections etc but what I am looking for is people's positive experience. Perhaps their doctor telling them how big their baby was and ending up being much smaller? Idk. I have friends who delivered vaginally and who had sections so I have the good and bad from them both.