So I only play normals and it seems lately whenever I team up I get teamed up with some silvers, golds, and sometimes plats. So does that mean my MMR is up there or it's just plain random?
There is an MMR for normals, but since this is generally where people play with their friends, and the rankings are so varied, you'll often see any range of player anyway. (A diamond player who plays with bronze players a lot will have a lower MMR than someone who only plays with other diamond players in normals, for example.)
Similarly, I do believe Twisted Treeline and Dominion also have an MMR. I am unsure about ARAM, but I know that Team Builder also has it's own MMR separate from blind or draft pick.
Your MMR could have gone up. I'm thinking the same thing for me, because I'm constantly being paired with golds in team builder and ARAM (I dont play Dominion)
Similarly, I do believe Twisted Treeline and Dominion also have an MMR. I am unsure about ARAM, but I know that Team Builder also has it's own MMR separate from blind or draft pick.