Hi,
Sorry you feel like this, and very very sorry about your cat. Our cat is family and every bit as important as a human. Getting news of a loved one's severe illness is deeply upsetting so your feelings of irritability and anger are understandable.
But, as you point out, they don't help with making friends and overcoming loneliness.
Are you on medication? If not, would you consider it? I found ADs took the edge of that anger at the world and made it easier to be more relaxed around other people, so that I could socialise and feel more connected with the world.
Have you tried signing up for free CBT self referral on NHS - no need to contact the GP. It takes a while for your turn to come up (about 3-6 months) but is well worth it, especially if you choose to focus the six sessions on pne particular issue and goal, eg making friends.
Sorry if this is obvious advice, but are you treating yoruself with love and compassion> i know it's a cliche but it really is true that we make friends more easily when we have committed to being our own best friend - by that I mean treating yourself with kindness, respect and compassion - taking care of your body, your environment, allowing yourself treats and opportunities, facilitating proper relaxation. I spent years learning this - took me way too long - but am pretty good at it now and it really does help. if you;re interested in chatting about how to do that, I'm here.
Otherwise - have a little rant on here. I have to go soon but will check in later and loads of other people will come along. MN is brilliant at MH support. It is MN at its very best.