Yes. Shiva Linga can be kept in your house but you must follow some rules to keep Shiva Linga in your house, as we invited Shiva into Linga by doing Prana Pratista.
Dr.Annadanam Chidambara Sastri gives some instructions one must follow to keep Shiva Linga at home. This video is part of Telugu Program called Dharma Sandhehalu which is aired on Bhakti TV.
Lord Shiva has two forms. Akalam and Sakalam. Akalam is Nirguna form (unmanifested) which is worshiped in Linga. Sakalam is manifested form with Goddess Parvathi as Parameswara. It is said that by anointing Shiva Linga with water and offering Bilva leaves to linga (placing those leaves on top of Linga), we can tie Kamadhenu in our house. There is no Dosham in keeping Shiva linga at home.
It is suggested to do Abhishekam to linga and offer Bilva leaves daily. If you go to other place, you can immerse Shiva Linga in rice. It's not mandatory to know Namaka-Chamaka Mantras (Sri Rudram) to do Abhisheka but heartfelt Abhisheka with water is enough. Make sure the Puja Room is clean and sacred.