Paying for a co-working space as a sole trader is just like a business renting an office - it is quite normal. The social environment (either as a result of co-working or using a traditional workplace) can have a positive effect on productivity, but as one might expect with the human condition, no-one can say for sure how it will work for you. You may find that the increased productivity will fund your co-working expenses, but again it's not possible to say.
Here in the UK we have not embraced co-working as much as we should have - I believe it is much more popular in mainland Europe. However, we do have a number of such spaces, and it is quite normal to be able to get a guided tour of the facilities. I would recommend visiting as many spaces near you as you can. You may even find, as we have here, that some co-working spaces will give you a few days free of charge, to "try before you buy".
As an alternative, consider finding a set of coffee shops and working from these, perhaps in rotation. I've done that for some years, mixing it up with a co-working space, and the change of scenery in the early afternoon can be useful, especially if one is concentrating for long periods of time. That said, the economics of buying coffee-shop coffee and lunch can get rather expensive: here it's easy to spend 10GBP/day, which is 200/GBP a month, and yet a co-working membership can sometimes cost as little as half that (outside of London, of course).
If you are cost-conscious, some co-working places will do a part-time ticket, and you could split the time between working from home and the office. This is sometimes sufficient to boost your productivity, even though you're still working in your apartment some of the time.