My problem came mostly from how I lived apart from the people I most commonly interacted with so social opportunities were few and far between, eventually I realised that I just needed to make more of an effort. Bug people enough initially and eventually you slip into that "should be invited" section rather than the "nice they came" section.
I've been a bit lazy about developing new friendships in my current situation and as a result my active friend circle has shrunk drastically. I'd be welcomed at parties with my acquaintance/friends but it's unlikely I'd be actively invited as I don't make any effort to be part of that 'group'.
What procrastination said. I struggle with this too. As I've gotten older I've realized that a lot of people were interested in being closer friends earlier, but thought I wasn't interested because I was 'reserved,' 'standoffish,' or 'private.' It has been a matter of learning to let down my guard with people, be more open and comfortable, and stop feeling ashamed about not 'getting it' like everyone else seemed to.
As far as getting in touch with your emotions: For the longest time I "decided" what I was feeling in my head, which can be kind of dumb. A key moment for me was when I was going through a period of time of stress and hurt but was largely in denial about it; I was sitting on a couch and feeling horrible. I told myself, "Why do I feel sad? I'm happy." It didn't take long for me to figure out there was something wrong with that statement.
You might try interacting from an emotional rather than intellectual level. For example, let's say there's someone you'd like to become friends with. If you did something exciting last weekend and they seem interested, tell them about it but make sure to enrich it with descriptions of the emotions you felt. If the other person is more of a "feeler" than a thinker, what might happen is they start to connect with those emotions too. They might then want to share a time when they had a similar emotional experience. This is a great opportunity. Listen carefully to their story. Ask questions that focus on their state of mind/feelings/context. If something they say triggers recognition in yourself ("I've had the same thoughts/feelings/dream/etc") but don't distract from their story too much.