my cat has just gone missing about an hour ago. he is an indoor cat and sometimes goes in the back garden whilst being observed (back garden is just a square with walls/fences on all four sides and a shed). my mum went into the garden an hour ago and left the door open behind her and went back inside within 30 seconds. all doors and windows are always closed

yesterday some people came over and my cat is afraid of strangers. i thought he was upstairs but he was downstairs and saw the people entering, while running around them to go upstairs he hit his side quite hard on a door frame. i checked on him by pressing his side and he had no reaction so i assumed he was okay. i kept an eye on him in case of any later symptoms. this morning about 2 hours ago, he was meowing for food so i gave him a few pieces of dry food as a snack before his food would dispense 30 mins later. after 20 mins of him eating the few pieces, he vomited. he was okay (still his usual energy and activity and still meowing for food) so he then ate his food approx 10 mins later. after that is when my mum went into the garden. he is not the type to immediately go running outside unless he sees a bird/cat. i’m worried he is either injured and hiding in the house or that he escaped without anyone hearing or noticing. he has never been able to get out of the garden as he’s not much of a jumper so i have no idea if he’s outside or inside.

i have checked his usual hiding spots and everywhere and anywhere he can fit. i shook his food, said his favourite words and have left his bedding and litter outside (i was told to do so by someone at his microchip company.) i’ve registered his microchip as cat missing, messaged neighbours and alerted a neighbour app. i don’t know what else to do, if anyone has advice please let me know