Hi OP,
Firstly, there have been many amazing replies with great advice in this thread which I hope have helped you :)
I'm sorry that this is an older thread I am reviving, but I felt really compelled to respond and hope that my story will help at least a little bit, to reassure you that someone in a similar position has been ultimately able to enjoy visual activities even with the floaters being very distracting :) 
I have really bad floaters, almost like a 'swarm', sometimes it feels like a misty, webby cloud swooshing across my vision when I move my eyes. Have had them since I was a teenager (I'm short-sighted) as well, and I'm like you, almost all of my hobbies are visual (art, video games, looking at nature, my job is looking at a computer screen, etc).
My degree was also in illustration, so I spent many days in a bright white studio looking at bright white paper to draw on, and subsequently being distracted by the swooshing of the floaters going across my eyes! 
(I also have bad anxiety/depression/OCD for the same amount of time.) /end background
The reason I'm writing that bit of backstory is that I had similar anxieties to you - grief over not being able to see clearly, worry about whether it would get worse, etc etc.But - as others have said - the moment I begin to get distracted, I can't 'see' them anymore. I don't mean that in a 'just don't think about it' way, as that's like telling you not to think of a pink elephant, but more in the way of it won't physically stop you from seeing the nice things you want to see. :) Your brain can ignore them when you look past them.
I wanted to reassure you by saying that many many times (as I've got used to them over the years) I have looked up at the sky, at a sunset, flowers, animals, trees, blossom etc and thinking 'Wow, that's beautiful', both with and without noticing the floaters as well.
I won't lie, as others have said I do still notice them, and sometimes it is a bit of a 'tch' annoyance moment, but it's seconds/minutes at the most now, and maybe once every week or more, rather than multiple times a day as it was at the start. As time marches on, I'm sure it will be the same for you too, once this wave of anxiety begins to die down.
I also have obsessive-compulsive disorder and amongst other things/anxieties that go with it, I also can't ignore scratches and smudges on my glasses and want totally clear vision. However - as I am short sighted, have floaters, and also have minor double vision in both eyes (which also upset me for a long time), well, my perfectionist nature is having to come to terms with that!
If I can manage it - anyone can! 
Maybe try making yourself actually focus your eyes on an object that's pleasing to you (which I know is hard when you want to track the floaters instead). Really -look- hard at that tree, flower, landscape, try to notice details in it, and if a floater gets in the way, maybe blink/look around a bit, acknowledge it's there and go back to focusing on the object again. Sometimes I also find giving my eyes a quick look side to side a few times 'shakes' them out of the way long enough to distract me from them if I'm having an anxious day.
Another thing that's helped a bit is paying more attention to sounds and smells and textures of things that please you, such as a nice spring breeze, tasty food cooking, your favourite throw/blanket, cuddling your family, etc. It's a nice non-visual distraction sometimes if you really can't ignore the floaters at that moment.
Finally - and I hope this has indeed been the case for you since you originally posted - "This too shall pass.", both the anxiety and the floaters :) (I can never remember where that quote is from, but it has helped ground me in the past).
Wow - that was a long post! Apologies, and I hope it isn't too rambly to read and helps a little. All the best to you