Goodness...I feel like I've posted so many of these...Anyway! Here's what I remember from the story!
-Kagome finds a demon baby in the forest while traveling with her group (I think that the pup is lying next to his dead mother)
-She takes him along and he wont stop crying (I believe it's because his aura is so weak...maybe)
-Sesshomaru stumbles upon the group with the pup and stays to help (after some persuasion?) by giving the pup some of his youki and or surround the pup with his aura
-Later on Kagome falls down the well and Sesshomaru is left to raise the pup alone
-The pup does not speak at all but when Kagome returns he says Mother and races to the well.

...For some reason I feel like Ive mixed two stories together. Lol! If so I would love to know the name of both! Thanks yet again!!

urgh... I know that one...... but..can't...remember...name...

I know what fanfiction you are speaking of, but unfortunately I can't recall the name of it. I am currently looking, but have yet to find it.

As far as i can tell, you may be mixing two stories. The las two scenes you describe, are most definately from Bound to Love By Blood by Brandypandyxxx
www.fanfiction.net/s/5097375/1/Bound-To-Love-By-Blood
Rated M on FFN

It may be on dokuga as well, but its bookmarked for me On FFN

your fisrt three scenes arent part of that story (well, at least not the way you described them). But it does involve a demon baby, that is given into kagome's care (not found beside a dead mother, because he doesnt have one. He is a pure blood demon. Sesshomaru basically created him). Sesshomaru eventually travels with the group for the child's sake (not necessarily to share his aura, but because he is the father). Instead of the baby constantly crying, they are actually a little worried because he NEVER makes a sound

Kagome is sent through the well, sesshomaru is left to raise the child, and eventually when she comes back, he says "mother" and races to the well to meet her.

This is actually one of my favorites, and i think im going to go read it again!

I just read this! Its "Pack Instincts" by witchenmoon1

The jewel shards are taking three years to collect and along the way Kagome finds something interesting. She just might need the help of a certain daiyoukai to figure out what to do with it. The final battle with Naraku is approaching!

Rating: M - Universe: Canon - Status: Complete - Category: Chapter Stories - Genre: - Updated: 06-05-13 - Created: 05-07-13 Chapters: 24

Thanks soooo much two!! <3 Sorry about the mix up in facts though >.<