I use the interest from my bank account to help the needy around me and to help my friends who are needy. I do this without any expectation of reward since I know Riba is Haram. Should I continue or discontinue help in this manner?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Riba (usury/interest) is on of the major sins. Allah strongly declared its prohibition and announced war against the one who indulges in Riba; such a person is also cursed in this world and the Hereafter and Allah threatened to eradicate blessings from his wealth. Allah says (what means): {Allah destroys Riba} [Quran 2:276]
How could a person make such a bad act as a means to good deeds? The Prophet said: "Allah is Tayyib (which implies pure), and He does not accept except that which is pure."  [Muslim]
There is no doubt that if the means is forbidden, then it is forbidden to use it in order to achieve something even if it is Islamically required. This is like stealing with the intention of giving in charity, or depositing money against interest with the intention of spending the interest in a righteous cause and the like, then the objective of such acts is not taken into account as long as the means that leads to it is forbidden.
If you do not want any reward from your help, then what is the benefit of your act? Know that you will not only miss the reward, but commit a sin, expose yourself to the curse and lose blessings in your wealth that is resulted from dealing with Riba if you continue doing such a heinous act.

Allah knows best.