Total means "no part of man escaped the consequences of the fall." By "Total Depravity" we mean that all three parts of man, body, soul, and spirit, have been damaged by the fall and thus lack the perfection to enter heaven apart from the Grace of God. It does not mean every lost person is as bad as he could be, just that his body is fallen, his soul is fallen, and his spirit is fallen.
What you have described is classic "Particular Redemption."
The atonement is "sufficient for all" (sufficient propitiation for all mankind) but efficient only for believers (the elect) (the individual human being).
Unconditional election means that
man meets no condition of perfection to come to Christ apart of the Grace of God. God, according to the good pleasure of his will, grants Grace to whom He will grant Grace.
Romans 9:18 So then, he has mercy on whom he desires, and he hardens whom he desires.