I'm sorry that you're struggling financially.
It's great that you've managed to buy your own house. It's unfortunate that your mortgage payments have increased so significantly, but hopefully that's just a temporary thing, and rates will start to come down again. I don't think you should downsize. Sounds like you're managing the mortgage payments ok, albeit you don't have much disposable income. As time goes by and your salary increases (in line with inflation), your mortgage payments will be lower in comparison to your salary. Also, in the early years, you're paying a lot off the interest. As time goes by, the interest will be less and so raised interest rates won't have the same impact.
How long will you be paying back the student loans? Are we talking months or years? Is there light at the end of the tunnel?
Paying hundreds a month to lease a car isn't ideal. I'd be looking to change that a.s.a.p. Even if it meant taking in a lodger for a year or two to fund a decent, second hand car. Not a brand new, top of the range car but also not a rust bucket - something that will last a few years without incurring high maintenance costs. Are you locked into a contract with the lease company? If so, I'd be looking to have a plan in place to buy your own (second hand) car, by the time the contract expires.
There's only one income coming into your household, so all expenditure has to come out of one salary. That might change if you meet someone and can share the household costs. But of course, if you end up having children, you'll have to take on childcare costs or else sacrifice the second salary. Swings and roundabouts..........
Previous posters have suggested a second job or working overtime. But if you've spent seven years training, I'm guessing you have a medical qualification? Which means you're probably working very long hours already. So probably not an option.
Without access to a detailed breakdown of your expenditure, it's not possible to say if there's any room for leeway. The usual things suggested are shopping at a cheaper supermarket, switching your utility suppliers frequently to avail of new customer offers, cancelling Netflix/Sky/Amazon subscriptions etc.
But perhaps you're not looking for advice? Just frustrated that your salary doesn't give you the lifestyle you expected at your age and given your qualification(s)? Which is fair enough.