I would suggest that you let someone record your sparring on video. Often there is a big discrepancy between your own perception what you think you do and what you actually really do. So watching yourself on video you can see whether your trainer is actually right in his observation.
Then, yes, you should get used to get punched in the face, because that's just part of the game and you won't be able to avoid every punch, BUT you don't necessarily need to take punches to the face/head deliberately.
For your training Halfraq9 is right. Not only as a beginner for your technical improvement it is necessary to do your sparring at a pace and intensity you can handle without getting under much pressure, so you can focus on your movement. As you get more comfortable you can raise the pace and intensity. Talk with your training partners about that.
And HexRei is also right, there are many different ways of handling incoming punches. Some people just close their guard, some run into them, trying to brawl and to land punches themselves and others try to be as elusive as they can. Things you should be aware of, if you have the habbit of moving your head back. Having your head up exposes your chin, so it might be easier to hit it. If in addition you lean your whole body backwards you might get out of balance and you get into the danger of your opponent just rushing forwards keeping his attacks going on an eventually hit you then.
But overall it's hard to give you specific advise without having actually seen you spar. So if you have the possibility, make a video and maybe load it up on youtube or somewhere else, so people here can give better advise.