You've received great replies, I'll just add that if this must be a DIY effort due to budgetary restrictions, there are several resources available, for background information, teacher-led activities, and books for children, which could form the basis of a book-club style discussion group:

Emotional Needs
The book Emotional Intelligence by Daniel Goleman, 2005.

The book The Essential Guide to Talking with Gifted Teens, Jean Sunde Peterson Ph.D., 2007.

Booklet of Self-scoring Emotional Intelligence Tests.

A caption in the Seattle Times article linked by another poster, "Students in schools using RULER get higher grades in language arts" plus mention of "The Feeling Words curriculum" on the Yale RULER website brought this book to mind: The Emotion Thesaurus.

Peer Relations
Many have found the books The Gifted Kids' Survival Guide for ages 10 & under, The Gifted Teen Survival Guide, and 101 Success Secrets for Gifted Kids to be helpful.

Perfectionism
With regard to your other topic, perfectionism, you may have read this elsewhere on the forums...

Perfectionistic tendencies may be a sign of developing a fixed mindset rather than a growth mindset. One aspect or application is that gifted kids may stop taking appropriate risks in order to always be "right" or always be "smart" or never be "wrong", and this may work against them. The concept is nicely summarized in these youtube videos:
Ashley Merryman & Po Bronson: The Myth of Praise (link-
)
Teaching a Growth Mindset (link-
)

Parents may wish to read the book Mindset by Carol Dweck for tips on promoting a growth mindset.

A book which seems to understand perfectionism very well and which many find supportive is What To Do When Good Enough Isn't Good Enough. Another book you might like is Perfectionism: What's Bad About Being Too Good. While insightful, these are written gently for kids, in a style that is fun and engaging. With any of these books it may be wise to pre-read and decide if it seems to be a helpful tool to use in guiding the children you have in mind.

Procrastination can be closely related to perfectionism.

Helping a child consider "worst case scenario" and finding various work-arounds to keep moving forward... may in some cases help reduce the child's anxiety and add an element of self-confidence, even a sense of looking forward to taking on the challenge.

The article, 10 Steps for Parents and Kids to Tame the Worry Monster Daniel B. Peters, Ph.D. on Huff Post Parents, discusses anxiety. Interested readers can sign up to receive updates from the author.

The book, Make Your Worrier a Warrior, (2013, Great Potential Press) authored by Daniel Peters Ph.D. lends expert insight to understanding what a child may be experiencing. For example, pages 44-45 suggest that parents may wish to think of acting out as
Quote
a variation of the "fight or flight" response... children couldn't articulate their fears... they were reacting behaviorally because their amygdala, or their emotional brain, was overriding their thinking brain... kids often do not have the emotional vocabulary and/or insight to tell you what is going on...
Armed with this knowledge, working on helping a child understand nuances of feelings and vocabulary to express their interpretation of what they are experiencing, may prove helpful.

Here is a post and another post from other threads which discuss a few more potential resources.