I have put on many shields on many different phones and NEVER had this problem. Maybe being more careful when you apply the shield would be your best bet.
Hardly. Rice absorbs moisture kid and has proven to be effective in these cases. A blow dryer is a bad idea because it heats up too much and can ruin the otherwise delicate electronics. Also, since the OP was asking for advice and was told not to turn it on but did anyway, whatever damage that could have been done is done (if any at all).
Installed BSE front cover last night.. I used minimal water, and turned my phone on this morning.. when on a white screen I see water seepage on the bottom left corner of the screen! Will it dry out??