Hi Jennie

As Stellajane says your hair loss could be due to the hormone in Tibolone.
Some of the progestogens in HRT are androgenic ie stimulates male characteristics ( such as baldness etc). Here is the information on this site about the different progestogens:
http://www.menopausematters.co.uk/perimeno.phpProgestogens which can be used cyclically are of 3 main types:
Testosterone derived - Norgestrel, Norethisterone acetate and Levonorgestrel.
Less testosterone related - Medroxyprogesterone acetate(MPA).
Least testosterone related - Dydrogesterone and Micronised progesterone (Utrogestan).Tibolone is mildly androgenic so this could definitely be having an effect.
You haven't said how old you are but it sounds like you are a candidate for a different type of HRT (oestrogen patch or gel maybe - or at least a tablet like Femoston) and supplementing with very low dose of testosterone (for libido) - under medical supervision. Some women find libido improves with HRT, but less so with oral HRT I understand, and the synthetic progestogens can also interfere with libido too.
Also have you had your thyroid levels tested? Hair loss can be a sign of something wrong here? I would expect though that you would have other symptoms as well as hair loss if this were the case.
As the doc says HRT can also improve it but not an androgenic one!
Are you able to get a consultation at a menopause clinic in your area? it sounds like you need specialist advice for menopausal symptoms as well as hair loss.
Hurdity x