I'm a pre-university individual.
About a week ago I cold-emailed university professors inquiring about interning at their biology research labs. A professor replied on the same day expressing possibility of an interview. He also made it clear it would be unpaid - which, after some thought, I've decided I'm fine with. Long story short, I was stupid and indecisive, and only emailed him back a week later, with an email looking along the lines of:
Dear Associate Professor X,
I'm really sorry for the delayed response; I’d hoped to get back to you sooner. I've thought about this. I very much am grateful for your kind willingness to consider and would be pleased to meet up with you to better present myself, and work something out together.
If it's not too late, when would you be free to meet? I promise not to dillydally again. I am free this entire week. Just let me know a time that works best for you.
It's been about 2 days since I sent this reply, and he hasn't gotten back to me. When he first replied to me, it was on the same day I had sent him my first email.
Looking at my reply, I realize I forgot to thank him (for his time and consideration) at the end of the email. Ending my email off the way I did could have made me seem entitled/presumptuous.
Dear reader, was my reply rude/presumptuous? I'm really worried I've offended him somehow. I'm thinking of waiting a day more, then sending him a follow-up email that includes an apology or something. Should I?
Is this a gone case? What could I do to salvage this?
Thank you all for any input.