I shower everyday and wear deodorant but the pits of my shirts always smell after one wear. If I'm wearing the outfit for long enough, pits of sweaters and jackets will smell too.
I try to wear mostly cotton. The smell is way less intense than when I wear other fabrics. They all have different effects - polyester is the worst, rayon is doable but I need to plan around it (for example, I will wear a shirt underneath/ won't wear it when I'm going to need to walk around a bunch). I think people are often different in this regard so maybe figure out what's really working better for you? But I pretty much accept that if my sweater smells after I wear it, I'm going to wash it.
Once, the pits of my ponte trench coat got kind of smelly and I wanted to wear it for longer without putting it in the wash, I soaked the pit areas in vinegar and a little cold water and then rinsed the areas out and hung it next to a fan so the pits would dry. It worked to get the smell out. Also like someone else said, vinegar in the wash works very well if smells persist even through wash.