I've never heard of Litugest as part of an HRT regime???!!! Are you UK based?
Actually a 50mcg patch should give you all the protection you need for the bones and heart. You might want to try Utrogestan vaginally for 12 days each month as this may result in a more effective shedding off the lining and might prevent the erratic bleeding. If you are getting erratic bleeding then either the progesterone dose isn't enough or you may have fibroids or polyps - in which case a scan would be a good idea to ascertain what is going on. If you really want to increase your oestrogen levels then having a Mirena fitted might solve a lot of your problems as it usually results in no bleeding at all after the first few weeks - which can be a big plus - and you can then use as much oestrogen as you feel you need. I'm not always convinced that high oestrogen doses give that much benefit. Diet, exercise and relaxation can do more good for our general wellbeing than anything else.
I had a premature menopause and I found the Mirena with 2 pumps of Oestrogel was my best HRT regime. You do need HRT if your are oestrogen deficient before the age of 50.
Dry skin could be a lack of Vitamin D and Omega 3 oils and if you are lacking in these vital elements then fatigue, aching joints and dry skin are indicators for this deficiency.
Central heating and cold winds do strip our skin of moisture as well.
If it is 16 or more days since you last had progesterone, then I would start the Utrogestan, however if you are bleeding you may have to take it orally and this should be 200mcg (2x100mcg capsules) taken before bed on an empty stomach. Once you have the bleeding under control then you could try using it vaginally.
Here is the section on this site that explains about how to use Utrogestan.
https://www.menopausematters.co.uk/to_progestogens.phpDo stick with the sequential regime as using a continuous regime (progesterone every day) can bring more side effects. Utrogestan can have a sedative effect.
I would ask to have a scan though as you need to know why you are getting erratic bleeding - adding in the extra oestrogen will encourage more bleeding. DG x