I never had appendicitis but my daughter and my grandson both did. My daughter was more complicated by the fact that she had chronic appendicitis. She would get the bad abdominal pain, vomiting and low-grade fever. The Emergency Room would hook her up to an IV and while waiting on test results she would start to improve. This went on for about 3 years until they did a CT scan and finally did surgery.
My grandsons was similar but his was over the course of a few months. His mother put it off as anxiety issues from starting High School and trying to make the Baseball Team. He never told his dad what was going on. Then I got a phone call that he couldn't stop vomiting, no fever, but he refused to go to the hospital. After almost 24 hours of this my son flipped out and told him if he had to call 911, he was going to the hospital. I met my grandson and his mother at the ER and knew immediately it was serious. The doctor walked in, and I just asked when the surgery was scheduled. He had to be transferred to a Childrens Hospital since they didn't do pediatric surgery at that hospital. I drove my son to the hospital in the morning and we just missed my grandson going in for surgery. Thank God my son fought his ex and grandson because the appendix ruptured overnight. They were able to flush his abdomen and put him on a very powerful antibiotic. As scary as it was, he ran a very high fever for about 24 hours but those meds when they kicked in were fantastic, we were able to laugh. While still in pain and fighting the fever he threw me out of his room and made me go to his baseball game. He wanted me to tell the coach he really tried to hold off til after the playoffs, teenagers. I also had a Disney trip planned so he wanted a special gift - a sword from China. Grandmom got him what he wanted.
Knowing the seriousness, I would err on the side of caution and at least go to an Urgent Care.