I’m very aware it doesn’t work like this, but for the sake of argument.
If your mother wanted to be a grandmother then why didn’t she have more children to increase the odds of one of you having a child. If you’re her only child and all she’s ever wanted is to have a grandchild, then that’s her bad planning. You don’t want children, but she could also have had a child who wasn’t able to become pregnant, didn’t live to adulthood (slightly morbid I know), had a child but refused to let her see them.
That being said, at 16 I was adamant I didn’t want a child. There were a lot of people in the family with serious side effects (including near misses with death) from pregnancy. I was told I would need daily injections during a pregnancy. Now I’m 26 and I’m leaning towards having them, I’m not saying you’ll definitely change your mind, but I found when I had a partner and some stability I stopped being so against it. A fear of pregnancy is a perfectly valid fear.
I’d suggest you stop talking to your mother about it for now. At 17 I doubt any doctor will tie them. At 18 you can start looking for a doctor and you’ll be old enough that she has no say.
A future husband is not a consideration. For me knowing I have someone who would be a great dad is a minimum requirement which made me think I could do it, not the point where I had to. It’ll probably rule out a relationship with the guy who wants 5 kids, but you could equally want kids and not be able to have them. Would this theoretical partner also leave then? If you get your tubes tied and meet someone who could be a long term partner then you can casually mention it and let them decide. I had to tell my partner I might really struggle to have kids, his response was that we could get 2 dogs (or adopt a human child) instead.
Although nothing is going to change your mind, maybe you could try talking to a therapist about your fears. You could still be afraid, or you could improve it and decide you still don’t want to give birth and that’s fine. But as you seem to want children in the future, you might want to consider if you would still not want to give birth if you weren’t afraid anymore (some fear is normal). Surrogacy and Adoption can be hard and expensive.
In the meantime for birth control, take two methods. So pill/implant/coil and then condoms in addition.