It does sound like she is depressed, poor thing. I would start by working on the bonding process. You can do this either through food or through play. If she likes tuna give her a tuna treat when she lets you touch her, or she sits with you. Most cats go bonkers over freeze dried chicken - you might want to try them with her since they're not as messy as tuna. You can also find tuna flakes or fish flakes which she might like as well. Other than snacks I would not mess around with her food too much right now, sudden changes in diet can upset the tummy.
Spend time playing with her with a wand toy every day, at least twice a day if possible. Try to do it at the same time each day so that she learns the routine. If she likes to play fetch that's a good game as well. After a few days she will probably look forward to these times shared with you, and this will help her bond to you.
BTW, not all cats like to be held or petted. Give her space if that's what she wants, and let her take the lead as far as how much physical interaction she can tolerate. If I recall correctly you are her 4th home in her short life so she's probably learned not to bond to people, which means you will need to be patient, loving, and understanding of her needs until she learns that she can trust you, and you won't be leaving too...
Spend time playing with her with a wand toy every day, at least twice a day if possible. Try to do it at the same time each day so that she learns the routine. If she likes to play fetch that's a good game as well. After a few days she will probably look forward to these times shared with you, and this will help her bond to you.
BTW, not all cats like to be held or petted. Give her space if that's what she wants, and let her take the lead as far as how much physical interaction she can tolerate. If I recall correctly you are her 4th home in her short life so she's probably learned not to bond to people, which means you will need to be patient, loving, and understanding of her needs until she learns that she can trust you, and you won't be leaving too...