Need — require (something) because it is essential or very important rather than just desirable. The need feels like you will not make it through this pain if you do not have the desired object near you.
In grief there are things that we do because we need them as part of our healing process. It is not uncommon for us to wear his favorite shirt for 30 days straight. Because I need to feel his presence in my heart.
Want — have a desire to possess or do (something); wish for. I want this shirt. I have found memories of him in this shirt.
Over time these needs even if they are strange to you. (i.e., not wanting to clean out their hairbrush) will slowly turn into wants. I want to place his shirt under my pillow as it comforts me.