on the hunt for baby probiotics!

Amy • Married💏 proud mommy to a bright baby girl 😍
I have a 12week old and I am trying to find a good probiotic, not filled with filler crap. 
Anyone giving their babies a probiotic? Reviews? Suggestions? 
I will discuss it with the pediatrician first, but I like having an actual product I plan to try before I talk with him about it. 
Noticing some eczema starting on my 12 week olds arms. I'm trying to use the aveeno eczema baby lotion.. but I'm not seeing much help from it. I read that probiotics can help this. 
Thanks in advance for any suggestion!