The original basis for the right to have your case heard (“non-refoulement”) is article 33 of the 1951 UN Convention relating to the Status of Refugees:
No Contracting State shall expel or return (“refouler”) a refugee in any manner whatsoever to the frontiers of territories where his life or freedom would be threatened on account of his race, religion, nationality, membership of a particular social group or political opinion.
I don't know much about US law and practice in this area but this principle is broadly accepted and applied, e.g. in airports in Europe. However, it only means countries have to consider an application if the person can't be sent back to the country they are coming from. On a land border, if you are not threatened in Mexico, it's not obvious that it applies.
To the extent that Mexico is deemed a safe third country by the US, you could therefore be denied entry and handed over to the Mexican authorities, at which point Mexico could in principle decide to deport you back to Malaysia or let you claim asylum, but in Mexico. In practice, I have no idea what kind of treatment you can expect in Mexico. Presumably a lawyer or support group could tell you more about what works and what does not.
Technically, the US is not party to the 1951 convention, but only to the 1967 New York Protocol, which refers back to article 2 to 34 of the convention.
