A letter of intent almost certainly won't help.
@gonnif can give you a great explanation, but it boils down to this:
- You applied, so they know you're interested
- Adcoms assume that LOIs are baloney, as discussed in this thread:
LOI and Interviews?
- If you don't have any other acceptances, an LOI is meaningless because you have no alternatives with which to bargain (i.e., you'll go anywhere you get an acceptance since that's your only choice)
There was a recent thread where we discussed the difference between letters of interest and letters of intent:
Letter of "interest" ?. It's worth a read-through.
As for whether to send an update letter, my gut feeling on the updates you've got:
- GPA: noteworthy only if the increase is significant
- Psych minor: adcoms won't care
- Honors notation: probably won't help much
But for definitive information on that, look for guidance from gonnif,
@Goro,
@gyngyn,
@LizzyM, or
@Med Ed.