I have the following ideas of how to solve this problem:
What do you think is the best option to present a product image carousel alongside previous/next buttons for nearby category products?
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Is it an app or responsive website?
Why have Next / Previous icons to select products. The indicators below inform the user there is more to view and to swipe left or right to view the next product while still remaining in the catergory. The area you are using to place the icons would be better used for navigating the app.
If the icons go anywhere it should be on the image itself to prompt the swipe.
Responsive Website: Why have Next / Previous at all? Scroll. Keep it simple.
There are lots of examples online showing how to display products, interact and navigate.
www.rudys.paris is a good example. The navigation is simple. The indicators inform the user there is more to see before making the decision to purchase. No more than four clicks in from the home page and three from the catergory. The more simple the design the more simple the experience and the easier it will be for the user to make a purchase. Do not complicate the proccess. When money is involved you want the user to feel in control, informed and confident.