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It was a combination of the two.

"and he fed him with his own hand upon living flesh, and put his power upon him. Swiftly the worf grew, until he could creep into no den, but lay huge and hungry before the feet of Morgoth. There the fire and anguish of hell entered into him, and he became filled with a devouring spirit, tormented, terrible, and strong." (The Sil, Of Beren and Luthien)

"Nothing hindered him, and the might of Melian upon the borders of the land stayed him not; for fate drove him, and the power of the Silmaril that he bore to his torment." (ibid)

So the initial strength that Morgoth gave to Carcharoth caused him to grow in strength, but it was the torment of the Silmaril that caused his terror to grow sufficiently for him to penetrate the Girdle of Melian.

Glorfindel, by maddening the wolf, the Silmaril did increase his strength, or at least the manner in which he used it.  Carcharoth became a much stronger enemy because of the disregard he showed for his own body once the torment of the Silmaril gripped him.  So even though he didn't grow physically stronger, he used more of his existing power to press the attack without regard for defense.

That is indeed true, here is a quote:
"But Carcharoth looked upon that holy jewel and was not daunted, and the devouring spirit within him awoke to sudden fire; and gaping he took suddenly the hand within his jaws, and he bit it off at the wrist. Then swiftly all his inwards were filled with a flame of anguish, and the Silmaril seared his accursed flesh. Howling he led before them, and the walls of the valley of the Gate echoes with the clamour of his torment. So terrible did he become in his madness that all the creatures of Morgoth that abode in that valley, or were upon any of the roads that led thither, fled far away; for he slew all living things that stood in his path, and burst from the North with ruin upon the world. Of all the terrors that came ever into Beleriand ere Angband's fall the madness of Carcharoth was the most dreadful; for the power of the Silmaril was hidden within him."

"But now a shadow fell upon the joy of Doriath at the return of Lúthien the fair; for learning of the cause of the madness of Carcharoth the people grew the more afraid, perceiving that his danger was fraught with dreadful power because of the holy jewel, and hardly might be overthrown."
(The Sil, of Beren and Luthien)

As we can see the fact that the power of Carcharoth was increased by the Silmaril is presented here twice. Even though it burned him, the "holy jewel" gave him a "dreadful power".

Atavarne, a pure person with a clean soul like yours would have nothing to fear.
But maybe your soul isn't so clean after all my lady...

no it is not, and if you haven't guessed it already here is another quote:
"And Varda hallowed the Silmarils, so that thereafter no mortal flesh, nor hands unclean, nor anything of evil will might touch them, but it was scorched and withered"
So you see the Silmarils only burned those with unclean hands and evil.
Of course they also drove some mad, but also only because they were evil.
So if you are pure my lady you have nothing to worry about.

by the way you are spamming I doubt you are very pure...
but the good part is you have no Silmaril, so you don't have to fear anything.