Like most of sub-Saharan Africa, Somaliland harbors an array of tropical diseases of varying degrees of severity and inconvenience.
Although there’s a fair possibility that you will become ill at some point on your trip, the cause is most likely to be either straightforward travelers’ diarrhea or a cold, and provided you receive the necessary immunizations before you travel, the only major cause for concern, once you are in the country, is malaria, which can be combated to a large extent by taking sensible precautions.
Within Somaliland, there are private clinics and/or hospitals in all the larger towns, but they tend to be under-equipped and overcrowded, the main exception being the private Edna Adan Maternity Hospital in Hargeisa (ednahospital.org).
Pharmacies are also present in all the larger towns, and they are usually quite well stocked and staffed by an English-speaking pharmacist. You should be able to buy such commonly required medicines as broad spectrum antibiotics and Flagyl in any sizeable town.
If you are wandering off the beaten track, it might be worth carrying the obvious with you. As for malaria tablets, whether for prophylaxis or treatment you would be wise to get them before you go as not all tablets are readily available.