It's very common in research to only measure a subset of the Big Five. When I recently reviewed the literature on the Big Five and well-being, there were a huge number of papers that only used a subset of the Big Five. And I'd say that the most common variables to be measured in isolation were neuroticism followed by extraversion. More generally, if I were to add one more to the mix in health related research, I'd say that conscientiousness deserves greater attention. It's particularly relevant to health-related outcomes and captures quite a different mechanisms (e.g., compliance with treatment, healthy lifestyle, lower levels of compulsive behaviours, etc.).
And when you look at this research, they generally take scales from standard length measures of the Big Five (e.g., NEO FFI, IPIP NEO 50, BFI or BFI 2, etc.). You also have Eysenck's measures which are still popular and provide neuroticism and extraversion measures.
That said, I'm not really a fan of this piece-meal approach to personality measurement. It's not that hard to include a complete measure of the Big Five, and then you get a more comprehensive view of how personality maps onto the constructs of interest, rather than assuming a priori that the domains you're looking at are all that there is. If the number of items is a big issue, the BFI 44 is not that long or if you get desperate there's something like the Mini IPIP 20 (although alphas are a bit lower). We discuss these recommendations and trade-offs quite a bit in Anglim & O'Connor (2019).
Anglim, J., & O’Connor, P. (2019). Measurement and research using the Big Five, HEXACO, and narrow traits: A primer for researchers and practitioners. Australian Journal of Psychology, 71(1), 16-25. https://psyarxiv.com/a78g2/download?format=pdf