5 years ago I became Muslim, al-Hamdulillah. 10 years ago I had 3 tattoos made on my arms. Now I would like to know if it is better to have them removed or to leave them. I ask this as I don't feel comfortable to show my bare arms in public, but I have also read that it's not good to mutilate your body. Would removal of tattoos by plastic surgery be classed as mutilation or not?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions. 

You should remove the tattooing if that is possible and does not have harmful side effects.
Ibn Hajar al-Haithami said: 'When the disbeliever had tattoos before becoming Muslim, he should remove them when he becomes Muslim' . In fact, anyone who does tattoos on his arm or elsewhere, this part of his body becomes impure at engraving and his prayer is invalid as long as he can remove the tattoo.
Allah knows best.