Even a free flowing sink can have smelly crap in the u-bend. I have this very problem right now, although it is not as smelly as yours, I don't think.It's not blocked.
I'm not great with home DIY stuff and you may think you need a plumber to take pipes apart but I learnt that it's actually pretty straightforward and will be the quickest way to sort out the smell.
Yup, I've done that!Oh yeah and don't go to wash it out in the sink you just disconnected the drain from, like I did. Twice.
I spent the weekend on a comparable problem. You might have Object(s) stuck in there. This kind of thing might help. I bought a 10 metre one for £20. Being narrow and bendy it can get round corners. Maybe even a U bend.
But dismantling the pipes would be best. You'll never be sure what's in there unless you do. And you can use a scrubbing brush to every bit of cack out.
Could you post a photo of your under-sink pipes and describe the pipes they lead to? What floor are you on?
Every time I’ve taken a U bend apart I’ve failed to put it back together again without achieving a torrent of water coming from the joins