How do you get used to getting punched in the face?

I love going to the gym and picking up new techniques but I find that I've focused primarily on wrestling and BJJ. Not that those are bad styles but I want to become an efficient MMA fighter one day and I know my stand-up leaves much to be desired. There are Muay Thai and Boxing cles offered at the gym but there aren't many opportunities to spar during cl. My instructor said that next month he will add more sparing but I've tried to spar before and it just looks awful. I often turn away and leave myself vulnerable. The guy who I sparred with told me, "it only hurts as much as you think it will" but I'm not sure if he just said that to make me feel better. It's a shame because I hit very hard and would be a great striker but obviously it's harder to punch someone who's fighting back.