Yes, Instagram requires app review approval before your app can access live data, but that mainly applies to other users' data. If you're just working with your own Instagram account (the one that generated the access token), you can typically test API calls without app review. However, you must have the right permissions and a properly generated access token.
Regarding your OAuth errors:
If you're using the Graph API Explorer, make sure you’ve requested the necessary scopes (instagram_content_publish for publishing media). If your token is from a personal Instagram account, it won’t work—Instagram requires a business or creator account connected to a Facebook Page.