Your classification is part of your rich journey as a student. Reflect on why it is important to you. Reflect on why you got the grade you did. Think about how you can use that knowledge.
I was possibly a little like you and missed out on a 1st due to extenuating circumstances. It has made me always encourage people to seek help when they need it and submit extenuating circumstances forms. It also made me more determined to see potential and encourage that spark - I know the encouragement of one of my tutors made all the difference to me. It also helped me in my other degrees to know my physical limits and to look after myself as well as studying.
A masters might help you, especially if you think it will affect your career, but how would you feel if you didn't get a distinction? A PhD is only worth it if it is on your career pathway. Most of a PhD is just slog and determination.
I think that the people who really value a 1st probably aren't aware of how fine a line it is. Yes sometimes students get 1sts who are truly exceptional, other times a really good student might have a bad year or a good student might really work hard and push themselves into the first classification.
You might watch JK Rowling's speech on failure to Harvard it has some interesting points about failing and the benefits of it. Before anyone jumps on me I don't think the OP has failed but to OP it may feel like that. Reflect on this as an opportunity to understand yourself as a learner and to build your determination. It will make you stronger as a person and will help you to face future adversity.
Don't lie about it, you would only really be lying to yourself because no one else particularly will care what classification you got, unless on a CV and you could lose your job if you lie on a CV.