So i'm currently using a 100mm -6deg ITM XX7 Stem on my fixed gear bike and my brother is suggesting a 110mm -10 degrees to fit me properly and for the geometry of the bike to be parallel, I'm currently at 5ft 7in, in terms of height, the bike frame fits me just fine as far as everyday use is going but there are times that i feel my arms and palms to be a little sore at times but not all the time. I just wanted to get your opinions on which should i follow. So one picture there is what the bike geo looks like, the second is me riding the biking and what i look like when riding it, I hope to get your opinions soon.

I would say the fit looks good as is except your arms are straight with no bend at all. As a trial, I'd try to flip the stem over, which would raise the bar a bit, and see how your arms feel.

I don't know, that stem looks already flipped over in the direction that raises the bars. What I notice is the back angle of the rider could be much more acute. When you see a rider with a nice bend in their elbow they are much more bent over at the waist than this rider is. So it doesn't appear that there is much more to be done with respect to hardware.

Your reach does look short and sore hands indicates you're putting too much weight on them. I suggest first leveling the saddle. It's tilted down and you're probably pushing with your arms to keep from sliding off the nose. While you're at it, you might also try sliding the saddle back a cm or so on its rails. Your fixie has a track geometry with a very steep seat tube angle, so sliding the saddle back for everyday riding would help.

Then revisit the stem length. You're not tall, but the bike looks short and your back and arms look a bit cramped.