You don't actually appear to be taking anything that would cause an addiction or a suppressed immune response. Of course with any supplements, it's preferred to get them from nutritional sources.
If you do have worries, it would be with the NO3 chrome because it is more than just arginine. It may be best to find an L-arginine supplement that you are OK with. The ingredients in NO3 chrome basically has sort of a boosting effect on the NOS activity of arginine so if you aren't putting this too a use (I.e. working out or something similar) it's not really a cost effective benefit.
As far as immune responses, if these are the only supplements you are taking, both are beneficial to immune health. Arginine-derived nitric oxide plays a major role in inflammation and immunity. I'm not sure where you heard about negative effects on the immune system but it could be something along the line of high doses of nitric oxide having an inhibitory effect on T-cell mitogenesis which theoretically wouldn't be an issue with an actual L-arginine supplement. It can also be noted that arginine enhances the phagocytic ability of certain immune cells too, increasing their protective response. Omega 3's are already well know in their ability to help battle inflammation but they also have been shown to enhance immune response by increasing and activating a number of immune cells in the body, increasing a person's ability to fight infection. I should stop here before I start giving an immunology lecture lol but if there are any questions about this I would be happy to take a stab at them.
L-arginine ALONE has not been shown to have dependent characteristics not has Omega 3 fatty acids. This does not take into account consumption of these supplements with other chemicals such as caffeine. Arginine and Omega 3 fatty acids can both be obtained through food consumption.
I hope I made a slightly complicated question a little more understandable.
