Most definitely do not feel like a failure - many women stoically sail through the menopause and either have very few symptoms, or cannot take HRT or do not want to.
However menopause is a hormone deficiency! Our bodies are being deprived of oestrogen that keeps us healthy! One of the main reasons to take HRT especially at your age is to replace the oestrogen at least until the average age of the natural menopause - around 50. This is needed to protect your bones from osteoporosis, as well as playing a part in keeping your bladder and ladybits healthy and supported! Taking it up to 50 doesn't count in terms of the maximum time which used to be recommended for women to be on HRT anyway (5 years) but this seems outdated now anyway. Many women take it for much longer for the same reason.
As your menopause was relatively early I would definitely take it for this reason, if there is nothing to suggest you shouldn't, as well of course to eliminate the horrible symptoms - and why should we put up with what is like an illness for maybe half our life?
Yes you may have to try a few - but if you go armed with knowledge hopefully you can make a good guess at what might suit you.
Do you prefer pills or patches? Have pills upset your digestions in the past? If so try patches? Are you allergic to adhesive? - if so try pills.
Did you suffer from bad pms and headaches before you periods? If so I would avoid HRT containing norethisterone (print off green menu to the left "HRT preparations" to take with you).
Don't be fobbed off with the cheapest eg prempak or premique - as these do disagree with some women and are less natural.
You might prefer to start with the cyclical HRT (look under perimenopause to the left) to see if you felt much better on the oestrogen only 2 weeks.
I use patches and would say I felt much much better within a fortnight - re flushes and sweats. Some other symptoms take a little longer to settle - but you should see a gradual improvement very soon!
Good luck with the doc and hope this GP in your practice is one of the knowledgeable sympathetic ones....
Keep us posted.