I think this is a phase that a lot of little ones go through - my DD had it at 4 months (she was premature and did everything later).
One thing to keep an eye on is sometimes it is not to do with being put down but wanting to be upright, as they can't yet sit alone. If babies have gas in their tummies, as most do, sitting upright (like when you are holding her) allows the stomach to become round and accommodating, whereas lying down stretches the stomach into a long, oval shape and reduces space, making the gas painful. As an osteopath I see this all the time with 0-3 month old babies and most of the time mums think the babies either hate their prams or are clingy when in fact they just need a whacking good burp.
Lots of mums stop burping the baby once they hear a burp sound after a milk feed but some babies (like mine) need two or three good burps to get it all out. With my DD, the burps kept coming even a couple of hours after a feed. I also found putting her slightly propped up when she was gassy helped, although they should not be propped up too high or for too long during the day. Is she ok when she is in a bouncer chair or when you prop her up with cushions and play with her?
If it is definitely not wind then I agree with the advice above - pick her up. Cuddle her and carry her around all day if you have to. It is just a phase and if she really is so distressed to be put down then she needs to be near you and to smell that you are there, during what is probably normal but nevertheless an unsettling developmental stage.
Final suggestion is a book called The Wonder Weeks, which explains all these funny, fussy phases that babies go through in their first 18 months and really helped me to realise that it is normal and babies are just clingy and unhappy sometimes but it doesn't mean she's not learning and developing perfectly and that she isn't a perfect, happy little girl.
Good luck!