DD is now 8mo but I completely remember those early days. You must get out and about and do this or it'll just create more fear and you'll be stressed every time you go out.
DD had bad reflux between 1-3 months and would just howl sometimes and in the early days I'd get so flustered it'd ruin my enjoyment of any outing. I think I was most worried about what everyone was thinking about my lack of parenting skills.
We joined a baby massage class when DD was 6 weeks and honestly, most of us spent the whole class either bf or cuddling crying babies! We were all laughing about how the only one doing any massage was the instructor! I made some great friends at that class and we still all meet once a week and go out for lunch, walks, picnics etc and even now, one or more of our babies will set off crying. But your amongst mums who have all been there so it's not as bad anymore.
Getting on the bus was my most stressful outing. If she started crying you can't just get them out of the pram easily on a moving vehicle. But take short journeys and build up your confidence. Worse case scenario you can jump off at the next stop, console your LO and get back on when they've calmed down.
Nappy changing is never easy in some of those public loos. I remember being in Costa Coffee changing DD and she was crying so much and kicking around it was impossible to get her clothes back on. It was taking so long someone knocked on the door and I decided that I'd forget putting her leggings back in and just stuck her back in the pram and walked back through the shop, past the queue waiting fir the toilet, with her screaming!! I found taking a toy or singing/tickling is a quick distraction. Also if you're out in town, John Lewis or similar have big baby changing rooms and you'll see lots of other harassed mums dealing with similar.
It just takes regular practice to build your confidence. What would you think if you saw another mum with a baby crying?? Bad mum?? Or 'poor mum, I know exactly how she feels'? And to anyone else/non parents, fuck 'em!! Babies cry...deal with it!