Yes, you are starting over again but that's okay. Now that you don't have anyone in the tank, you can do a fish-less cycle if you want. I'll PM you a cycle guide I wrote up. Hopefully it will help you decide if you want to continue cycling with fish or without. But don't be discouraged. Sometimes bad things happen to good fishowners. You're doing fine.
Cycling tanks takes a lot of time and sometimes you do have to start over once or twice before it cycles. And ich can happen to anyone at anytime.
Platies can be mean. :/ They are either really easy-going or just downright nasty. I have heard of a platy attacking a betta and injuring it so badly it died later. :( But right now I have three platies and a betta female in my 10g and it's actually my betta who is picking on the platies, so it all depends on the platy. If you can, get a few more platies so you have a group of 3-4. That will help spread the aggression around so the mean platy isn't picking on just one platy in particular. Or see if you can return the mean platy and get another one; maybe it will be nicer. Make sure they have some plants to hide in.
Did your female have clamped fins and was she kind of rubbing along things? She probably did have ich. My sorority recently had an ich outbreak but because it was all five girls, I had to treat them in the tank. Thank goodness I didn't have live plants but I'm thinking of adding some now.
If you have any more questions, don't hesitate to post or PM me. Hang in there, the road is rough but it's worth it when you get the tank all cycled.