This is a tough time of year for everyone in teaching, and it is OK to be feeling the way you do!!
As an NQT in a primary setting, I have been feeling similar myself - like I'm not doing enough for the kids, in spite of the 60 hour weeks I am consistently putting in. The fact that I am the first one there most mornings and the last one there, aside from the headteacher and the caretaker, still didn't feel like I'm doing a good enough job. Fortunately, when I discussed this with my mentor, she showed me some data and looked at some of the books with me, reassuring me that I was doing OK.
However, I am very lucky to have someone who takes the time to listen to me and help me. Without the other teachers at my school, I would be feeling much, much worse than I have been. We're a small school and so there aren't many of us, but we have really good relationships and know exactly who to go to for which support. I think this is a really key part of teaching - making sure that you have a good support network both at school and at home. Having friends who know how I'm feeling because they have felt it themselves makes my life so much better when I can have a rant
Similarly, the right team of teachers in a school means that your work is appreciated - I actually cannot count the times in even just 7 or 8 weeks that someone from the SLT has told me that I'm doing really well, or complimented some aspect of my teaching practise. Yes, some teachers are treated badly - but not all!
In terms of feeling bored... can't say I've felt that since I started teaching! Except for one day so far, when we had to do maths all day... that day, it was confirmed to me that I am cut out more for Primary than Secondary, because I get to teach so many different subjects instead of just one or two all day long! Is it possible that the boredom is linked to just having one subject?
Alternatively, it is important to make sure that you can have fun in your lessons, and if you have fun then your students are likely to respond positively to it, which will show in your teaching, progress, assessment etc. etc. Maybe something for you to focus on would be planning lessons that are fun for you? That might help with so many of the negative feelings you are having
Keep going - even if teaching isn't for you in the end, there are so many positives that you could take away from the PGCE year if you stick at it.