Cat inflammation on paw pads

My cat is 1 years old. I have taken her to the vets on several occasions over the last 4 months or so due to her paw pads being red and inflamed (picture attached). The sores have got worse since I took the photo attached, she is also reluctant to let me look at her feet now even though she is very comfortable and relaxed with me. She tends to lick them which makes them worse and they do look sore and the skin is broken in some places perhaps where her teeth have caught the irritated skin. The bottom of the pad is normal its around the sides of the pad where the problem is. She has had a course of steroids (1mg prednisolone) this worked really well and she took the whole course but over the last two days of the course she started with vomiting and diarrhoea. The v&d cleared straight away after she stopped taking the steroids and the paws looked a lot better so I thought that was it and she was back to normal. The paws have now started to go back to how they were. I have tried lots of things, her litter tray is always meticulously cleaned (she is an indoor cat), she has had her flea treatment, she has a good balanced diet, I don't use any cleaning products on the floor or if I do I always rinse it all down thoroughly. I'm out of ideas as to what it could be. My other problem is, she is very reluctant to let a vet examine her and gets very distressed so I was hoping that someone could offer me some advice or perhaps could tell me what they think the problem is. Of course I will take her to the vet again but they don't seem to get anywhere with her and now said to me that it would be hard to even sedate her so that they could have a look. She is eating, drinking and toileting as normal, isn't limping. The paws just seem to irritate her because she licks them a lot. Thank you in advance to anyone who reads this. I would be so grateful if there is anyone who could offer me some advice. - Anna