'Third world country' is an ambiguous term and a bit of a misnomer, because it originally meant 'a country aligned with neither West or East' (during the Cold War). Its use has become conflated with that of 'developing country', because the two meanings overlapped in practice. It is also considered derogatory due to its ambiguity and general connotation of colonial superiority.

It helps to be aware of those connotations if you choose to use a term like that (which can be a conscious choice to express your position). Although I agree that comparing it with racial slurs like 'nigger' is not really appropriate, there is some similarity in that these are words that are slowly moving out of the modern vocabulary appropriate for civilised discourse.

Just use 'developing country'.