But still, this is part of why I go out of my way to use deodorant without anti-perspirant. The idea of aluminum bits causing the pores to swell shut doesn't sound like a good idea.
It's bacteria decomposing the sweat causing the smell. Try anti bacterial soap in the armpits, washing t-shirts in 60+ °C hot water, drying on the line in sun, (exposure to UV will kill bacteria
If you want an alternative to slathering chemicals, look into essential oils. Also diet is huge contributing factor, albeit a longer path to find a solution.