Can i have new in-app products in my app without submitting the new build version?

As long as your app has logic to handle the purchases and product IDs

We are managing the purchase and product IDs, but the main question is that do we need to submit the new app version everytime we create the competition? Every week we create a new competition and in-app products related to it. So I don't think uploading a new app version every week is appropriate.

Please refer to Submit an in-app purchase documentation:

You can submit your in-app purchase or subscription to App Review as soon as you create it in App Store Connect.

If you're submitting your first in-app purchase or adding a new in-app purchase type to your app, you'll need to submit it with a new version of your app.

To submit an in-app purchase for review, it must have the Ready to Submit in-app purchase status. If it doesn't have this status, complete any missing information.

Learn how to submit in-app purchases and subscriptions with the App Store Connect API.