In English, the compound adjectives <NP>-<V>ing (noun or noun phrase followed by verb in its -ing form) and <NP>-<V>ed (noun or noun phrase followed by verb in its -ed or past participle-like form) imply different relationships between <NP> and <V>. Specifically, in the former case, <NP> is the object[note] of the action <V>, while in the latter, <NP> is the agent of <V>. For example, "man-made" implies that man makes (whatever follows), as in "a man-made satellite". If you were to say "man-making", it would denote something that makes man or a human!
But this analysis seems to break when the first element is the word "self". A Google exact phrase search for "self-driving car" currently returns about 6,980,000 results and a search for "self-driven car" returns about 540,000. While the latter -ed form is less than 10% of the -ing form, most articles appear to be written by native speakers, suggesting that both forms are accepted (but people may be subconsciously treating "self" as an object more than an agent?). After all, it makes sense because "self" means, well, self; there's no need to distinguish between agent and object.
The recent coronavirus causes pneumonia that is self-limited, according to China’s National Health Commission. So, let's check "self-limiting disease" vs. "self-limited disease", a term referring to a disease that runs its course without medical treatment (treatment may speed up the process, but that's a separate point). "Self-limiting" is slightly more popular than "self-limited", 118,000 vs. 105,000 on Google. Indeed, when the <NP> is "self", either the -ing or the -ed form of the verb is accepted.
[note] A more technical term for "object" here is "patient", not in any way related to a sick person in a hospital.