Careers in trading; how to pivot into it from AM?

Hey everybody, just a quick rundown on my background -- I recently started my stint for an asset management arm at a bank that has roughly 180B AUM for pensions, endowments, institutional clients, corporations, etc; the exit of this program is usually OCIO or liquidity solutions/fixed income management. I'm still very early into the program so I don't fully know what these entail.

I'm a graduate from a bottom-tier school with a finance major and no serious maths/programming background but always wanted to work in some trading/pure markets role which is what got me into finance in the first place; I've been trading a PA of my own for quite some time and have been a funded trader for certain funding companies for a few months. I know those aren't truly legit but only saying that to give an idea of where my interests are coming from.

I'm completely lost on the structure of the 'trading' industry in general and was hoping someone could break it down as I read very mixed things on here about the area. Is prop trading/discretionary trading an industry reserved for the quant/CS types these days? I've been told S&T at BB banks is market making with little to no prop risk; do they also look for the maths background?

I'm curious to gain some insight on 1) if prop trading/discretionary trading is still a thing for a background like mine 2) if so, what companies should I look into and how could I pivot into it from an AM background?

I don't really see a serious future for myself in AM since the pedigree factor is very serious; I don't plan on getting a CFA or MBA. I guess this shows my complete lack of knowledge for the industry but I really just want to hear out the different career options that has my work focused around the markets purely. 

Thanks.