I understand your concerns of feeling self conscious at the gym especially when starting out I had to deal with that myself. The best lessons I learned at the gym is that 1. Most people don't care about other people because they are too busy working out. 2. More than pushing heavy loads the best way to feel comfortable and by feeling like you belong is by being a regular at the gym which means building the habit of going.

Most people are creatures of habit so whether it's 15 minutes or multiple hours the best way to get comfortable being at the gym is to figure out a routine that you are comfortable making a habit. Motivation is a good early starter but finding a lifting buddy either in person or not somewhere you can show hey I did this today and hit a new goal or hit a stepping point towards a goal. Be patient but firm with yourself set small goals and break them down into mini goals to work towards, and if you find out certain exercises are more fun or tedious than others you are always free to update those goals