Does anyone with experience with eevee know what could be causing the light to bleed through my mesh at the top of the first image? It doesn't happen when I used cycles and it seems to move around when I move in the viewport
Yeah as Martin says it's a common problem in Eevee and it has to do with how it works internally and Cycles doesn't work that way so the problem doesn't exists in Cycles. There's settings in Eevee that will help you soften the problem, but it's all hacks and faking stuff, it's the nature of using real time render engines so don't be discouraged. Be sure to watch the Lighting course and learn everything about how to fix the light bleed and more.