I have few machines running ESXi 5.5.
On this ESXi I have two VM's
I only have ssh access to the ESXi, due to IT restriction I cannot install Vsphear client.
I need to get to Console of CentOS.
You may need to try new Host Client Fling,you can access your host using browser.As of now it for non-production host please refer the blog for more info.
Introducing the vSphere Host Client fling - VMware vSphere Blog - VMware Blogs
Perhaps you could enable ssh / open port (or it may be already open) on the CentOS/Ubuntu and use X-forwarding (putty) or / X-org.(Or use VNC?)
You can get to the DCUI from ESXi SSH but that's it. Not VM Console
You can use the host client as suggested above (not intended for production)
I'm assuming you do not have vCenter installed.
I've never heard of an IT policy restricting vSphere client. Anyone can access the client to DL from the ESXi host.