ERs are never first come first serve. They take people based off of severity. If someone comes in sicker or more injured than you they will be placed ahead.
Do not feel offended or unwanted. In the ER, they may prioritize someone with a serious condition that may need to be seen immediately. In addition, each provider sees dozens of patients at any given moment which explains long wait times as well. Hope this helps.
Thanks! Your answer is awaiting moderation.