Black/dark-red smooth West African worm, full of red blood
There are not so many potential candidate worm groups with similar appearance, namely: (free-living) flatworms, Nemertea and annelids.

While there are several terrestrial and freshwater flatworms, some of which are quite long, they do not approach such an elongated vermiform body shape and their mode of locomotion is different. There are around two freshwater nemerteans in Africa, neither of which looks like your worm, and in any case most nemerteans move by gliding using their cilia.

So the remaining group is Annelida. There are three groups of annelids relevant in this context: polychaetes, oligochaetes and leeches. Polychaeta are predominantly marine and normally have more or less pronounced parapodia ("limbs"). Some of the do behave according to your description, but they are very characteristic in their appearance and you would not expect to find them in a bathtub.

What remains are oligochaetes and leeches. Leeches are more or less dorso-ventrally flattened and have very prominent suckers. Moreover a fed leech (from which you would expect large quantities of blood) would look swelled (the gut in leeches has diverticula).

So, the only worm group I can reasonably suggest is oligochetes. In fact your worm looks and behaves very much like a common earthworm. It is very typical of them to be highly mobile during and after rains and their blood pigment is hemoglobin (i.e. red). The only contradiction is that your worm had no clear true segmentation, but I believe, in some forms it is easy to overlook it.

The fly is indeed some species of Psychodidae.