There is a POST method for to create comments, but it says the following:
Create a comment on a media. Please email apidevelopers[at]instagram.com for access.
See: http://instagram.com/developer/endpoints/comments/#
So do I have to get whitelisted for to be able to post comments or is the access_token enough?
Yes it is possible to post comments on Instagram via API. You have to get whitelisted now, so you have to email. This was not the case before, you were able to use commenting in api whithout whitelisting, but because of some apps spamming and abusing the comments feature, commenting now has to be whitelisted
See more: https://developers.facebook.com/docs/instagram-api/reference/media/comments#create