There are a few tools for such analysis.
It sounds that you need to measure your retransmission rates/dropped packets, latency components (server response, round trip time, payload transfer times, etc).
There are no tools that are free and can do all this well. You can download a free tool like Wireshark, but it does not provide packet header analysis of that depth. Unfortunately, tools like that can be quite pricey. I work on datacenter migrations and do these types of analysis for our clients all the time and well familiar with the tools on the market.
Network Instruments Observer allows this type of analysis to some extent, but it cannot provide detailed latency components.
Also, in order to see and analyze all packets on the network, you will need to be able to set up a span port on your access switch. All of the incoming and outgoing packets on your network should be copied/mirrored onto this port. I am not sure what type of switch you have as not all switches can be configured with the span port.
Another problem is that you also have VoIP. Some of the tools that I use for this type of analysis with the VoIP capability are Opnet Ace Live, Opnet Ace Analyst - but these are very expensive with the license cost into thousands of dollars.
I would say that Network Instruments Observer is one of your best bets. It is not as pricey as other tools and does do VoIP analysis pretty well. They do not publish their s/w prices online, you have to contact a sales rep for a quote.