I think part of it is introversion and part of it is social awkwardness.
You can fix social awkwardness but you can’t fix introversion, you can only work around it. Everybody finds different approaches.
Some introverts learn to enjoy certain groups. For example at the bar I go to there’s a bunch of introvert techies that hang out and chat in a small group. I cannot really participate in this activity. My ability to participate in groups seems to revolve around how well I know either the individual members of the group, or the topic of conversation that the group is speaking about. If it’s something I’m interested in I can engage. Or if I know every member of the group well then I can do ok.
Finding it weird to say I love you or hug is social awkwardness and will respond to just pushing yourself to do it a lot. I used to not be very comfortable with hugs but over the years I’ve come to tolerate, even enjoy them with certain people.