"Jesus healed the sick and dying and you didn't hear him boast about his actions"
That's because he never did in the first place. I challenge you to name ONE historian during that time period that even mentions a Jesus from Bethlehem performing miracles. Don't you think something of that magnitude would have made it into the history books?
Reminder: the burden of proof lies on the CLAIMANT.
To which I tryed to reply:
Besides Matthew, Mark, Luke and John (which there is amply evidence that they were written around that time or just after) there is also Josephus in his Jewish Antiquities 16.63-64 [the bits in brackets were probably doctored in by a scribe later]:
"At this time there appeared Jesus, a wise man [if indeed one ought to refer to him as a man]. For he was a doer of startling deeds, a teacher of people who received the truth with pleasure..."
Another translation here (chapter 3 point 3)
Also in the Talmud or baraitha Sanhedrin 43a-b:
"On the eve of Passover Jesus was hanged (on a cross). For forty days before the execution took place, a herald went forth and cried, 'He is going forth to be stoned because he has practised sorcery and enticed and led Israel astray...'"
Another translation here
So based on those two writings we have a guy around that time called Jesus who was suspected of sorcery and did "startling deeds"
(At least this way I can add hyperlinks)