Toddler screen time on a rainy day HELP

Do you let your toddler have more screen time on a rainy day ? My on is 3 and a half and it's SO HARD to entertain him in general but when it's raining it's damn near impossible. He doesn't want to play anything. He hounds me all day. I try to play with him I try crafts I try books I try everything all day and get nothing done because he is so miserable to entertain. I get so exhausted I give in and he gets more tv than usual. Then I feel like a horrible mom.

Also any ideas on entertaining a toddler that literally won't play ? He won't play by himself and he hardly wants to play with me either. Very very short tolerance for play. Then he hangs on me while I try to do chores and cries. I don't know how to entertain him anymore he never wants to do anything !! I dedicate my entire day to trying to please him idk what else to do. His doctor says it's just a phase but it's been this way so long. She says it's normal but I'm going insane !!!