Basically, after Ukrainian numerals, you use one of the three forms of the noun:

• you use nominative singular (до́лар) if the numeral ends in 1 (but not 11): сто оди́н до́лар '101 dollar',
• you use nominative plural (до́лари) if the numeral ends in 2, 3, 4 (but not 12, 13, 14): со́рок два́ до́лари,
• you use genitive plural (до́ларів) if the numeral ends in all the other numbers: двана́дцять до́ларів '12 dollars'.

Why 3 forms: In the past, all nouns had 3 numbers: singular, dual, and plural. Dual disappeared, but three different forms of the nouns are remnants of the system when it was still used.

Why 11, 12, 13, 14 are exception: Because they are formed differently compared to other nouns. Compare: 22 is два́дцять два ends in два, 32 is три́дцять два, BUT 12 is двана́дцять. This number doesn't end in два, it ends in -дця́ть (which is a reduced form of де́сять), so that's why we use «до́ларів» and not «до́лари».

N. B. These are not called suffixes in traditional grammar. Traditional Ukrainian grammar distinguishes suffixes (су́фікси) and endings (закі́нчення). Suffixes are used to make new words, endings are used to make forms of the same word. Each word can have more than 1 suffix, but only one ending. The traditional analysis is like this: here, we have a zero ending, -и ending and -ів ending (and no suffixes).

Some modern grammars call 'suffix' an 'derivational suffix' and 'ending' an 'inflectional suffix', so what you've said is not incorrect, but it's not how we usually analyse Ukrainian words.