I think it is highly unlikely that she's angry at you or finds you too much.

It actually seems she recognises that you are rather busy due to Uni constraints and is trying to accommodate. The scheduling issue is taking time as it needs some fine-tuning but it seems she is working on it too. Your idea re sending your June availability is a great idea btw. Maybe if weekends are free this could be considered as well?

I know it is awkward to wait around for a response but I am sure she will get back to you accordingly. Could you leave her a voicemail as well, if only to let her know you've emailed new June dates (once you've sent the dates)?