Old cat getting worse and worse every day?

I have a cat that will be 16 on tuesday and over the last 3 or 4 months he has started to develop a few symptoms that i am a little concerned about. It started with him hardly eating. And i dont think its because he just isnt hungry because sometimes he will go to his food bowl and just look at it so i started feeding him soft food which he would eat but now he is having a hard time eating that to. and what he does manage to eat he has a hard time keeping it down . he is throwing alot of it up. he is starting to develop a limp but that could just be from how old he is. My main concern is the sore he has on his back that wont go away. iv been told it was nothing but he is the only cat i have ever seen use his front pawa to rub a part of his body that he normaly cant scratch. and all around his back and side near the sore is really sensitive to the point of if u just barely touch him he bites at me. im not all that good with animals and i want to take him to the vet but i dont want to get there and find out it was nothing to serious money is tight right now so i cant really afford to take him to the vet but i will if i have to, any incite or advise from someone could give me will be greatly appreciated