AWS meaning Amazon Web Services? In an EC2 instance, or through Amazon RDS?
Are you connecting to your work network via VPN, or trying to access directly via the internet?
By default you're prompted to setup inbound IP restrictions when setting up resources in Amazon (you wouldn't want your SQL Instance directly exposed to the big bad web), so it's probably that your home IP address isn't allowed access, but your work IP address is.
I doubt you'd really want to be adding people's home (dynamic) IP addresses into the AWS firewall configs, so you would need to hop via your corporate network, either via VPN, with the correct config so the AWS address is routed via your corporate external IP, or another secure access method, e.g. Citrix/RDP to a computer on the corporate network with SSMS installed.
You can use telnet to check whether the basic network access is there, e.g. from a cmd/shell prompt "telnet <aws URL> 1433"