Your GP only prescribes those because those are the standard ones which they try everyone who needs them on. It's more difficult to get seen by secondary services, but I think you need to say to this Dr that if they won't try something else then maybe you need to be referred to someone else who might be able to help you more.
Did you take the meds at the same time each day? Not drink alcohol? Stay on them for 4-8 weeks? Not all agree with each person. My husband is on his 6th as the fluoxetine he'd been on for years didn't help when he went back on it... This one is helping him hugely though!
If you are genuinely fearful for yourself then surely you could get help if you were open and honest about it?
Why aren't you helping your Mum around the place?