It's down to personal choice. Want to cover up? Do it. Don't want to cover up? Don't. Makeup is expensive though, and rubs off on beds/hands/etc.
Scars are a lot like tattoos: you notice them at first in others, and then it becomes such a normal part of them and their skin that it's not eye-catching any more.
This is coming from someone who has a lot of (mostly white/faded, but a couple of red) scars on my body; has both dated a serious cutter and someone with tattoo sleeves respectively. You simply stop considering it after a while unless something new is added or it changes overnight. Kind of like somebody getting a new haircut/hairstyle - you probably don't notice their hair until that happens 
And tbh, I had mild complaints and questions about the black arm sleeve I was wearing to cover up the most visible ones, so expect that if you try covering them up with detached clothing. My latest are almost half a year old but their stark redness and size makes them look like they were made last week, so I covered up out of politeness to avoid people thinking I was seeking pity from something recent. Guess what? I had 0 comments about my scars when I took the sleeve off.
For most scars, their placement is obvious; people understand and respect what's happened, whether it's from surgery or something else, and if someone asks about it, the world's not gonna end. They're probably just curious about how it happened, why it happened. Interested people want to know the full story, but you're never obligated to answer or even acknowledge the comment in chat.
It happened, we got the scars to show it; we can't undo it, so we move on. I hope you feel 100% comfortable in your skin someday soon. It won't be overnight, so please be patient with yourself. Take care!
