With all due respect to the previous poster, the answer is actually 'not yet automatically'.
Facial Feminisation Surgery IS available on the NHS, but whether you can have it depends on what your local CCG is willing to fund. I presume you're in England; NHS England automatically funds certain treatments such as HRT, SRS, facial hair removal etc. because it calls these 'core procedures', i.e. they're essential in the treatment of Gender Dysphoria. But it doesn't automatically fund other procedures because it doesn't consider them essential, including facial feminisation surgery. So it is available, but your doctor has to apply for 'exceptional funding' in order to get it for you. And naturally, the NHS likes to be careful with their cash so there's a very good chance they'll say 'no'. Your best bet is to get as much expert support behind you (i.e. as many doctors from different disciplines as possible) to back up your case, and then push your CCG as hard as you can.
So you can apply via your GIC for thyroid chondroplasty/tracheal shave; rhinoplasty; facial bone reduction; and blepharoplasty/facelift. But as these are not 'core procedures' your CCG will judge them like any other application for cosmetic procedures and will (or will not) fund them accordingly. If you've heard of cases where they pay for cosmetic procedures to ease depression, it might help your case to bring them up. I daresay you'd need a formal diagnosis of depression in order to go down this route.
It's not all bad news though: up until relatively recently the NHS didn't routinely pay for facial hair removal. But after a lot of pushing from GICs it has now that's been declared a 'core procedure' so they have to pay for it. It's taking a while for that policy to trickle down to patients, but it is happening. And those same GICs are now pushing to do the same thing with Facial Feminisation Surgery, i.e to have it funded as a 'core procedure' so that it is automatically offered & funded. They know how important this is for women whose faces have been damaged by testosterone, so they're pushing hard for it. But the NHS is a massive bureaucracy, so it'll take some time before this is approved. Give it a couple of years, and you may well find that it starts to become routine.
Please don't be despondent. You can start saving up to have some of it done privately, and in whilst you're doing that the NHS may well start automatically funding the procedures you want done anyway. As StartingOver said, antidepressants would be a good idea (your GIC would want any depression to be under control anyway, so you may as well get started). As Laura said, HRT can help a little by changing the fat distribution in your face to soften its edges, and there may be some grooming you can try that might minimise what you're seeing. If you're not yet with a GIC, why not get on the waiting list so you can get the ball rolling?
