to my knowledge, there is really nothing in the server side that will reduce your running speed, lets say you have your knife out, the server/game will have a set speed for that weapon and will not allow other players to run faster than you. However a possibility is that the server has different plugins with different upgrades? Well I guess you would know if you play it a lot but I am just suggesting here. Also lag wouldnt affect this issue either.
The only thing that MIGHT be affecting you could be your configs, but that is only if you changed it. I am not exactly sure about csgo configs because I haven't looked into it yet, so I cant really give you the specific line of config to possibly change, but you can try deleting your config file which should be located under [Your drive]:\Steam\steamapps\common\Counter-Strike Global Offensive\csgo\cfg
Delete that file, go to your steam, right click on the game, properties, local game files tab, verify game cache and that should auto download a brand new config for you, but some of your settings might be changed.]
Hope this helped.