Should I give my cat away?

My beloved cat just died. She used to be an only cat, but then she got pregnant when we let her go outside, and we got rid of all of her babies but one, who happened to be very ugly, and no one wanted her. my mom would only allow one cat inside at a time, and bc the ugly one was only a baby, we let Harlee outside(the mother).Harlee was an exceptional cat, and we were all very much attached to her, but three days ago we found her dead outside my window.there were no bites on her, but she had blood coming out of her and her eyes were big, making me think she was very scared.its completely heartbreaking to me that i wasnt here to help her(i was at school), and that she came to me to help her, and all i can think is that she was wondering where i was and why she was in such awful pain.her kitten, Bug, who is about 7 months old now, was home when she died outside my window, and we think she watched her mom die, bc she stays by the window watching outside and cries. its gotten better for her, shes starting to play again but about twice a day she just sits by the window, and shes never done that before this happened. im completely destraught over my baby dying, that i feel like im not emotionally attached to the other anymore. and i dont know if shes salt in the wound everytime i see her and not the other, or if shes lessening the pain for me. but i kow that if i had the chance, i would give bug away for harlee to come back. im leaving for college in august, and would have to find someone to watch bug for me for 8 months, or have her putting in a boarding house, or give her away to a good home. BUT i also dont want Harlees death to be for nothing.(bug staying in, and harlee having to stay out, and me give bug away right after when i should have done it before harlee died, bc i had planned on keeping them both when i moved out, i just knew harlee was a good cat and she never strayed far from home, so i trusted that she would be okay outside) what am i feeling? is it just sadness about my other cat, and its leading me to think that what im feeling is ociated with this cat? or do other people feel the same way when a pet has died? and if you have felt the same way, did you give the surviving animal to a good home and how did you feel afterwards?