Painkiller is more commonly used as explained above, but I should mention that analgesic does not sound like anal because we pronounce anal or anus (the proper word for asshole) with a long a sound as in ape and analgesic with a short a sound as in apple. So, if you want to sound more scientific, go for it!

I can't choose a best answer. All answers is useful for me.

painkiller

The word "painkiller" is more commonly used. It is common knowledge versus the medical verbiage of analgesic.