You will be in no way "destroying [your] life". There's no point wasting time getting a degree that's making you unhappy, even if you are good at it. If you look at it in the long term, if you're having a miserable time now then the likelihood is you wont enjoy a job you get by doing that degree either.
If you know what you want to do then go for that- you only get one chance at life so you might as well spend it doing something you actually enjoy, but bare in mind that 2 years down the line you may feel the same way about bio-med as you do about engineering, you never know and it's a chance we all have to take in life!
There's nothing wrong with going to Man Met, or any other uni that isn't Russel group for that matter, I really think it's just something people say because you're in the same city so there's rivalry. It's like Man U and Man City football clubs, I'm sure the majority of people don't really 'hate' people who support the opposite team but for the purposes of rivalry (and football) they do. On the whole employers don't mind where your degree is from, it just matters what you got it in and what you got for it and as you plan to do medicine after they'll be more interested in that one anyway!
I really hope that helped to reassure you, do what makes you happy and don't care what anyone else thinks!