I am an Engineering student in co-op. This fall, my professor/employer recommended me to a company, they got back to me approximately 2.5 months later, offering me a co-op student position, but at this point it was too late since I had already accepted an offer for another placement and could not switch. Thanked them, explained the situation and asked them to keep me in mind for future, they said that they would.
Fast forward to 2.5 weeks ago, the employer sent me a message saying a position had opened and they would like to open this position to me for my next co-op placement and if I was interested to apply through a portal that was attached to the e-mail. I said I was very interested and applied the next day.
Fast forward to now, still have not heard anything back after I applied/replied to their e-mail.
So my questions are: Should I send a follow-up message? Also, do you think the most recent e-mail meant that they wanted to hire me for that position or just that it was available?
EDIT: Note that this is not me asking about following up after an interview.