If you haven’t already, you should become a social carer by offering customer support on social media.
Facebook and Twitter are great platforms to engage with your customers on a support level.
Personally, I would handle this on your main account so other potential customers can see that you care and support them, but you can create a dedicated page or account specifically for customer service.
Social is were customers spend most their time. Don’t make them search your site for a support number or email. Make it easy for them.