Don't beat yourself up, you ARE doing well! Every step you take towards getting fitter is doing something good for your body, regardless of whether or not you see instant results. When I first started to lose weight, I was often frustrated that it wasn't coming off fast enough. I wanted to see huge losses every week! Then, someone said something that really stuck with me:
"We don't put on all of this weight overnight, so we can't expect to lose it that fast either."
That really struck a chord with me, and it's 100% true. Losing weight is all about changing your eating/exercise habits over a long period of time. Little changes that you make DO add up. Try not to focus on negative things that people say about your weightloss efforts, you're doing this for YOU and no one else.
E.g. "Riding your bike will do you more good than going for your 'walks'." - Your mum probaly IS trying to be supportive by encouraging you to do the form of exercise she thinks is best. However, if you're happier walking, then that's what you should do. I for one hate riding stationary bikes, but I love getting out there and walking. Other people might find the opposite. I think the key is finding a form of exercise that you enjoy, and one that doesn't feel like so much of a chore. If you find something you like, you're more likely to continue it over a long period of time and incorporate it into your daily lifestyle. I used to force myself to go to the gym, and I absolutely hated it. I had a gym membership for 5 years, and about the only thing I lost was $2000. Now I just go for my "walks" too and swim. It's much more enjoyable for me.
Don't give up, you WILL eventually start to see some results. If you keep going with a healthy diet and lifestyle, the scales will eventually start to move down and you WILL start to notice a difference in your clothes. Next time you feel like your mum or someone isn't being supportive, just say something like 'thanks, but I think I'll stick to walking for today.' Eventually they'll start to notice a difference in you too. If you feel like you're not getting some support from your family, maybe you could ask a friend to motivate you/come walking with you? I'll be your weightloss buddy on here if you want, we're at a similar weight at the moment
I hope you're feeling better now, you CAN do this!