Condom broke 2 nights ago, found a piece of the broken condom this morning

Two nights ago I was with my fwb and we usually have sex quite a few times on our weekend get togethers. We were just getting started but the condom broke. He pulled out immediately and threw it away. He hadn't yet ejaculated but it's possible there could have been precum.

Anyway, this morning I went to the bathroom like my usual routine. It was normal. Zipped up, washed my hands and went to let my dog outside. Then I felt it. Something coming out of my vagina. At first thought it was discharge but thought it was weird considering just went to bathroom. But decided to to go to the bathroom again. I wipe and lo and behold it's the piece of the condom that broke! I thought the condom had just tore not like a literal piece broke off! I am also weirded out it was in there for almost two full days without my knowing. In part relieved to know it came out though.

I also take birth control, the risk right now according to eve is 3%, and I know my fwb doesnt precum or get wet as much as other guys I've been with in the past. I still know there is a risk, but I'm less worried about the pregnancy risk (though feel free to change my mind) than just knowing a piece of material can be up in there for a few days, and had it never come out on it's own, who knows if it would have caused an infection later on?!

Just wanted to share to get this load of information off my chest. Also should I tell him? The likelihood of something resulting from this incident is minimal and if something did I would take care of it.