You have cable in your room though, right? If so, buy another cable modem, split cable at wall and boom.
Does that add to the monthly Cox bill? If not that may be the best solution
Shouldn't unless you rent the modem from Cox. I would be surprised if they even found that you did it. From what I understand, they are able to tell when a device is hooked up, but it is on the back end of their filter/splitter for your house so it shouldn't raise any flags for them. That said, I haven't dealt with Cox for like 12yrs.
Also, it shouldn't hurt your signal unless you have a weak cable signal to your box now. I do this at my main tv in my house and get great pic and very good wireless strength.
You should be able to buy a Cable modem/wireless router combo for something like $180 or so. I use the Motorolla surfboard and it does everything I need it to do(bbs'n and twitter more than anything at home) and it has lasted a really long time(like 7 yrs so far).