adopted stray cat, not eating

i adopted stray cat(billu) i found it on garden, allowing me to pet him, it has been 9 day, yesterday billu was fed wet food, and my cat ate do quickly and later we take him bath after first time, after bath i went to somewhere and cat leave downward in some, where no family member is present it was morning scenario.

later what was sit upset and sitting in corner not eating anything i also noticed billu's one leg is paining he is sometimes is using his one leg but it is paining him he is not easily touching his leg on floor, and he did vomit yesterday whole wet food came out of her, and night time she also did water vomit 2 times, right now i am worried because she has not eaten and drinking anything from since yesterday morning wet food, just laying on bed sleeping with closing eyes

can someone help please, whether billu is fine or not