Don't put too much on your shoulder, you have certain self-awareness, and you've started to look for help, this means A LOT. This means you're on the right track. I think it's totally right to come to your GP for a plan and/or a referral to the psychologist.
There're something more I'd like to share:
1. Find a time, sit down, take a pen and paper, think deeply and write down a list of things which make you happy and unhappy. Especially for things making you happy, not necessary to be big things (e.g. finding your life purpose), it can be daily little things (having a walk in the morning and then hum a song while taking a shower). Once you write them down, you'll find that this process of improving self-awareness is healing, and will bring you more sense of control. It works for me and I hope it works for you too.
2. If you want to expand your social network, it's easier to approach the groups of people who‘s caring without asking anything in return. For example if you're Christian you can go to a church, if you have other religions find relative organizations. Or, try to be a volunteer, use your strength to help people, start with easy jobs. Your peers in these groups are more likely to be willing to listen, share and help.
3. I'm not sure if you have stress at work, if this is one of your major challenges, you can share your story. We'll see how we can help.