Would it be permissible for a black convert to immerse in the mikveh with cornrows(after ensuring it was clean) so as to keep their hair neat or must it be loose?
Before getting to your question, you should just know that a person that does actually make the decision to change their life, and become a proper ger, is loved by Hashem in a very special way. It is known that the Angles praise Hashem by saying “Kadosh, Kadosh, Kadosh, before they are allowed to say the name of Hashem, however the Jews are allowed to say Hashem’s name after saying two words, “Shema Yisroel Hashem…”. It is explained that the reason for this is that even though angles are holier than mere humans made of flesh and blood, however Hashem loves us more. The reason is since we have to fight our materialistic drive in order to do Hashem’s will, therefore we are loved in the eyes of Hashem more than angles. It is written that a Yitro, a convert, said Blessed (is) Hashem, and only prefaced hashem’s name with one word, why was he permitted to do this? The answer given is that the same way Hashem loves Jews more than angles, he loves converts more than regular Jews. This is because the convert gave up everything, and changed their whole life, for Hashem.
Regarding your actual question, the reason why a woman cleans herself before immersing in the mikva is in order for the mikva water to come in direct contact with her whole body and hair. If her hair is dirty, the water can come in direct contact with all of it, because there is dirt in the way. The same idea applies to removing any nots and for her to untangle and comb her hair.
This does sound difficult in your situation and preparing yourself for the mikvah is more difficult than it is for others, however, bear in mind, that Hashem will reward you more than 100 times more for your difficulty than the reward that other will get. The effort will be well worth your while.
Tractate Babba Kama 82a, Shulchan Aruch Yoreh Deah 198-1.