You really shouldn't be updating textures. You should have one or more static textures containing images of every possible inventory item, then every frame you draw specific items to specific parts of the screen with sprites set to use the right parts of that texture. Then just draw pieces of text around them for additional information like amounts. What made you decide to do this by updating a texture?
It sounds like you're trying to save the previous frame and change only what you need to change each frame, rather than clear it and redraw everything each frame. People often think they need to do the former for performance reasons, but they don't, and trying to do it that way makes their code far more complicated and buggy than it needs to be.
By the way, the most common uses of a RenderTexture are post-processing effects (eg, blurring the entire screen) and producing a static image at runtime (eg, if your user can customize his character's appearance, that appearance isn't changing every frame, so you can render it once and then reuse the result). I don't think either applies to a player's inventory.