I know allll about what lenses feel like when inside out....as the girl who did my 'training' taught me the wrong way (!!) and I didn't realise until a month later. You can still see fine, but yeah it's just scratchy around the edges though I found that eased after a while. Lol. When I put them in the right way for the first time I was so happy! I couldn't even feel they were there. I'd thought I was just gonna have to put up with the discomfort, accepting it as normal.
It's likely that your lens is scratched or slightly torn, (i only know about soft lenses though) they nick really easily! Also you could try removing it and giving it a really good rinse with your solution and then trying again. And also double check it's not inside out. Other than that, is it not possible to pop in to your eye doc when you can and see if there's an assistant who might be able to give u a hand?