If you delete your Instagram account, it will not directly remove your profile or any of your activity from someone else's Messenger view. However, once your Instagram account is deleted, any link to your profile that they may have accessed through Messenger will no longer work, and they won't be able to visit your profile or see any content associated with it.
Keep in mind that if they had already seen your Instagram profile or any of your posts before you deleted your account, that content would still be in their memory or saved to their device unless they explicitly delete it. If you have unlinked your Instagram from Messenger, it can also help in reducing any connections between the two platforms going forward.