Sound proofing can of course be done, but some things might be above your budget. There is a lot of discussion about this on different fora on the net, so you might do a bit of search. I suggest only one starting point here, the Sound-on-Sound magazine has done a number of articles on this (you might need to search a bit).
One solution is buy a sound booth. They tend to be a box within the room with sound insulation. There are several companies manufacturing and selling these. I give one link here only as an example, not suggesting anything as a recommendation.
Another solution might be to build a small "box" with a bit of insulation, maybe only for your head. There are a few of these to buy ready made.
Yet another solution is to sound insulate your room. It takes a bit of material and knowledge. Basically the room needs to be "water-tight" as sound will enter any little small opening. In addition you would want to "float" walls, floor and roof from the surrounding building. Finally, as it is totally air-proof you need to add some mechanical ventilation with sound traps in both air entry and exit.
In the end it depends on how much you want to isolats yourself from the outside sounds, isolate the world outside from your sounds insida and/or get a good sound inside your recording studio.