i've been on C for about 8 yrs. at first i had bad site reactions; lumps, reddness and pain. the medicine is pretty acid-y and that's why it burns.

i used to use the autoject for most shots. then the RN came out and taught me the manual, which i had resisted for some time, ok, yrs. but, the manual hurts a lot less.

i also used to ice mine but gave up on that. usually by 5 min's it stops hurting. make sure you're not pulling up on the skin. let it lay flat.
i use my free hand to "blow" til the alcohol dries. wet alcohol will burn.

you could even try some ice before you give the shot. just a couple of mins.
make sure you're injecting into subcutaneous fat. you may also need to adjust the needle depth. sometimes going a bit deeper will help. pull back if you don't have much fat. me? i've got plenty.

don't give up. it does get better with time. and, it becomes more routine.
pick a time of day that's convenient and try for the same time every day.
good luck.