I read something about them (mainly in Wikipedia), and I see some parallels in artistic style or symbolism, but I don't see a substantial parallel in their stories, although I didn't find much about the story of Sol Invictus. I don't see that someone was nursed as a significant parallel because almost every human was nursed.
I focused on parallels in their stories because I don't see parallels in the style of art depicting them as problematic to Christianity. But most of your previous comment was about artistic depictions, so, if you think that they are problematic, please, explain that more in details.
I don't have any experience with it, so I can't recommend anything, but I thank you for the notice of it; out was interesting to read about it on Wikipedia.