Do I need a family plan for Apple Music if I have just one person on my family plan ?

If you are the only person you don't need a family level plan. You are just paying extra money.

Click on the link to learn how to switch to a different subscription plan -->

From: How to switch to a different subscription plan - Apple Support

On an iPad or iPhone:

1. Open the Settings app. 

2. Tap your name, then tap Subscriptions.

3. Tap the name of the subscription that you want to change.

4. Tap See All Plans, then follow the onscreen instructions to complete your purchase.

For other devices, read the support article.