A noun appearing as N. fliw “sickness” in The Etymologies of the 1930s derived from ON. thlīwe < ᴹ✶slīwē under the root ᴹ√SLIW “sickly” (Ety/SLIW). The ancient initial sl became thl which was the usual sound change in (Old) Noldorin, and then this thl became fl, a less common Noldorin sound change. There was also a deleted variant of this root: ᴹ√LIW, where Tolkien had lhîw “disease” with the usual unvoicing of initial l in Noldorin (EtyAC/LIW).
Neo-Sindarin: In Sindarin of the 1950s and 60s, initial sl became lh instead of thl, so most Neo-Sindarin writers adapt this word as ᴺS. lhîw, as suggested by Hiswelókë’s Sindarin Dictionary (HSD). Based on the deleted variant of the root, I would use the word lhîw for both “sickness” and “disease”, both within a body and independent of it.
A word in The Etymologies of the 1930s glossed “lying in bed, bedridden, sickness” derived from the root ᴹ√KAY “lie down” (Ety/KAY). In The Etymologies as published in The Lost Road (LR/363) the glosses were “lying in bed, sickness”, but in their Addenda and Corrigenda to the Etymologies Carl Hostetter and Patrick Wynne indicated that gloss “bedridden” appeared between “lying in bed” and “sickness” (EtyAC/KAL).
Neo-Sindarin: For purposes of Neo-Sindarin, I would assume cael is the noun (= “lying in bed, sickness”) and N. caeleb “bedridden, sick” is the adjective.