I had the same problem as you, not so much fear of pain, but the fear of getting hit, or making a mistake.
The problem is your state of mind. Learn to EMBRACE getting hit, and understand that this is boxing, you WILL get hit, get bloody noses, get your wind knocked out, etc. its all part of the process. Everyone has gone through the trials and tribulations of getting beat up in the ring. Focus while you're in there, dont worry about the people watching you, dont be afraid to get hit, we all go through it. Its like learning stick shift, you are going to stall out, you are gonna ride the clutch, but its part of the process.
Ive gotten dropped several times, but we were going all out, not pulling any punches. One time it too, about 30 seconds for me to get off my knee, but i was more pissed off and continued sparring because i wanted to even it up.
Just go into sparring with a mentality of a brawler even if youre a slickster/ counterpuncher. Get your mind right and say **** it, what do i gotta lose.