You can either buy a cheap drain snake or maybe find somewhere that let's you rent them, but they can be relatively easy to break so that's probably unlikely. I'm unsure how big of an object we're talking here that might not be prone to breaking up so water can pass, in which case the drain pipes will probably need to be taken apart unless you could get it with a grabber tool.
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It's a bottle cap an also with me and my landlady both being disabled it's hard to do things that involve bending or squatting down. I think it's gone quite far down too.
Could maybe get it out with a drain claw if it hasn't gone down terribly far.

OK thanks for this suggestion. We tried this and although we couldn't find the bottle cap, this did pull out so much other gunk that the problem has improved, at least enough to actually use the shower.
If you're getting some water flow could try leaving a chemical drain cleaner like Draino in overnight.
We've tried several and they aren't doing anything. It's a drain with the hole on the side, it's hard to tip liquids into it.
depends what the object is really. If its just a clog of the usual suspects (hair and other small/soft debris) then a drain snake is probably the best option. it can't be too big if it made it down the drain in the first place (assuming your drain has a grate or some way of preventing large objects from falling into the pipe. I'd be shocked if it didn't.) Maybe post on local groups and try to find a kind handy person to help you out? you don't have to be a plumber to unclog a drain generally.
If you have a plunger you could try that too
It was a bottle cap
Magnet on a flexible stick. Or if it’s not a metal cap, use the grabby snake.
But there’s more at play here. A bottle cap stood on end should not block a shower drain as it should be at least double the circumference of a normal bottle cap. Thinking 30-40mm here.