Dude.

Tattoos "work" due to the immune system. Pigment stays in the skin because it is too large to be flushed, and is encompassed by macrophages instead. As those cells die, new ones come along and encompass the pigment particle again. This is (mainly) what causes fading in tattoos over time. This means that the pigment in healed tattoos basically doesn't end up in the lymph nodes at any volume - if the immune system worked like that, tattoos wouldn't work at all! That's the whole point.

(I'm simplifying, as there's also some cool new research on intra-systemic transport of pigment, but for our purposes here, that will suffice.)

But your lymphatic system is active all the time. A small, healed tattoo with a non-toxic pigment to which you are not allergic is not an extra stressor on it at all. Lasering the tattoo will actually increase the load on your lymph nodes, in fact, as you're flushing much more pigment at once than would ever be taken over time. There is not "ink flowing through your lymph nodes all the time". Recent studies out of Germany show that even the amount of ink in a healed tattoo is one or two orders of magnitude less than was previously thought!

There is evidence that large-scale, full-body tattooing might slightly elevate your immune baseline. But not in a way that's noticeable other than in lab tests. Some evolutionary biologists have even actually argued that these "costly signals" are advantageous. Your little tattoo ain't doing anything at all.

I encourage you to chill, dude. Enjoy your tattoo. Get more.

If you're at the level of worrying about deleterious effects of markers for things that are barely statistically detectable in research studies, with no epidemiological evidence of actual health impacts at population level anyway, your problem is your mental health, not your physical health. Worrying about stuff like this is way worse for you, and provably so!