You speak as if Mexico doesn’t have its own problems with racism/discrimination/prejudice/etc against its indigenous peoples
Latin America has its own history of racism. On the whole, more subtle, less in-your-face, less over-the-top extreme, than that of the US, but still very real
Mexico can and does have its own problem against its indigenous people, and the situation under a supposed "merger" (not that it will happen) can still get much worse.
Mexico has its own equilibrium and power balances regarding its racial issues, grown over the centuries, that wont be transferrable to 350 million different people, a good deal of whom would consider the whole population, latinos and natives, as inferior and "not belonging here", and has worse skeletons in the closet regarding the treatment of its own natives.
Well, hypothetically speaking (given we both acknowledge a US-Mexico merger is rather unlikely to ever actually happen): yes, it could be worse, maybe even “much worse”; but it could also be largely the same; it could even be better.
One way in which it could be largely the same: the remaining racism in the US is largely of the subtle/systemic kind rather than the blatant apartheid/Jim Crow kind, which makes the racism problems of the US and Latin America much more alike today, despite historically the former being drastically worse than the latter
One way it could be better: for all their limitations, American tribal governments actually have significantly more powers than their Mexican equivalents - federally-recognised US tribal governments are partially exempt from state jurisdiction, while all Mexico has is indigenous-controlled local governments with significantly less legal autonomy. So you could argue that the US shows greater (albeit still limited) respect for indigenous peoples’ rights to autonomy and self-governance, and if a merger of the US and Mexico happened, it might result in that US approach being adopted in Mexico too, resulting in improved rights of autonomy and self-governance for Mexico’s indigenous peoples
How does that figure? It's not like the US doesn't have its own drug violence, and lots of it. A lot of Mexican drug violence would probably move to the north, where the more lucrative markets will be, especially since movement would be much easier.
>solve Southern Border problem
It wont solve it in the sense of addressing the concerns behind those seeing it as a problem today: it will just declare it not a problem.