I'm not so sure if this'll fix the issue with the old mod's blood textures being used instead of this mods', but you seem to need help fixing this addon. Although I have no experience coding in the source engine, I think what's going on is when host a server with the addon, the addon starts using the textures from another addon. No idea why the original addon used this code, but if you look into this addon's files, if you go into the folder named "lua", and then "autorun", you'll find a .lua file named "autorun.lua". I'd assume this automatically runs when you load into singleplayer/multiplayer. If you open this file (with something like notepad++), you'll find this.

// Damage screen fx - Coded by mrfish
if CLIENT then
include("cl_damagescreen.lua")
elseif SERVER then
resource.AddWorkshop('773286171')
include("sv_damagescreen.lua")
end

It seems if you are a client, on singleplayer or on a server, the mod uses the file from the "lua" folder, "cl_damagescreen.lua".

If you are a server, hosting a multiplayer game, it downloads the workshop file with id "773286171". When searched up in the workshop, this id goes to a mod called "Screen Damage Materials", which seems be the textures of the old mod. Change this to your mod's id so it uses your addon's files.
It should look like this:

// Damage screen fx - Coded by mrfish
if CLIENT then
include("cl_damagescreen.lua")
elseif SERVER then
resource.AddWorkshop('2881944092')
include("sv_damagescreen.lua")
end

I'm not sure if this'll break the mod entirely when hosting a game, but i'll check if it does.
All i know is it fixed the issue for me, but i was on singleplayer that time. I also checked the rest of the lua files and "autorun.lua" is the only one with any mention of the old mod's workshop id. The texture issue also only started when i hosted a multiplayer game for me and my friend, and persisted in singleplayer.

Hope that helps.