Scared I may have been exposed to rabies after finding weird thing on cat

Yesterday night, I noticed that my cat had a dark piece of debris on his tail. This is not unusual, but normally it is just a piece of leaf or mulch as he spends a lot of time outside. However, it was intertwined between his tail hairs (he has fairly long hair), and when I yanked it out, it took a lot of hairs with it, so it must have been sticky initially. When I looked at it, I noticed that it was not just black but that it had some dark red parts as well. To me, it resembled a tiny piece (about 0.5 cm wide, 1 cm long) of jerky or some other kind of smoked meat, and it was also very thin. I started to panic because I had no clue what it was, and I broke it into pieces. Then I put it close to my face and sniffed it, which was a really stupid thing to do, but it didn't smell like anything. As I looked at it closer, I noticed that there was one little black hair in it that I could see after I broke it apart, and it was not one of my cat's hairs as he is orange-white colored. I have no idea what that piece could have come from, and there is no way for me to find out, so I am terrified that it was from a dead bat and that I may have been exposed to rabies. I was really panicking, my parents had a look at it and they didn't know what it was but they insisted that it was nothing to worry about. My dad made me throw it in the toilet, but I forgot to flush the toilet, so I came back about 15 min to look at the pieces in the toilet. When I picked them up, they didn't feel hard anymore and felt, and looked, a bit more like fragments of a dead slug or something. I thought that maybe it could initially have been a squashed slug that my cat's tail picked up outside that dried up, since my dad said he saw the black piece on my cat's tail since early in the day, but I know slugs don't normally have reddish blood when alive, so I doubt that it turns red when their bodies dry up. Also, where did the black hair come from? I really am terrified that it could have been a piece of flesh from a dead bat and that I could have been exposed to rabies. I am so scared because there is no way for me to find out what it was, I got rid of the piece so it's not like I can have it tested or whatever. I am at work but I am thinking of going to the doctor afterwards and asking for rabies post-exposure treatment. I really don't want to die, there is so much I haven't experienced, and I don't want my parents to have to bury their child.

Wow... you've really created quite a fantasy here. With respect, being that rabies has all but been eradicated in modern civilization and you absolutely cannot contract it by sniffing something, I'd say your parents won't be burying you anytime soon :)

Positive thoughts

The only evidence you have for a being a bat is that it was black and had a black hair in it.

But what about every other numerous rodent out there that is black and has black fur? Isn't it much more likely it could be off them, especially with it likely being rubbed up against by your cat?

It could even more dirt & gunge that is everywhere on the ground and a black hair has somehow found it's way onto it.

Plus how would you catch rabies that way?

A short read on rabies will make you realise quite how absurd a fear this is.

Try and analyse how your thought processes led you to panic about something so irrational.

Use this as an opportunity to learn.

I mean this in the nicest and most reassuring way here, but your fear here is ridiculous. Put it immediately out of your mind.