I've been using Ernie Ball Power Slinkies (11-48) for a while on my guitar. I usually have it tuned Eb or drop C#. However, my new band plays in drop B, so I've been tuned down to that. I noticed the first fret or two on my higher strings has sounded dead, so when I looked down my neck, I see that it is bent a bit.

I'm assuming that the change in tuning is to blame. Is this the cause? Would getting heavier strings alleviate this? Or should a simple adjustment of the truss rod take care of this problem?

Thanks in advance.
Ibanez Xiphos XPT700
Laney VH100R
Epi Les Paul (SH-1 '59 neck, SH-11 custom custom bridge)