As long as you are looking for consultancy, private clinic may be good, but when it comes to real treatment as well as diag., i advise HMC-Women's hosp.
Approach to nearby health centre with passport and electricity bill, pay QRs100 and get health card. It's very easy process. Once done, they will do few blood tests and start the normal treatment. If anything serious, they will forward your case to Women's hosp.
Hope, this will clarify ur doubt.