I still haven't received any money and I am worried that they may not
reimburse because I didn't take the offer.
Is that possible? Should I just send an email and ask them?
It's possible, although very unlikely. Few companies mess around with reimbursing these sorts of expenses - the small amounts aren't worth the negative reputation they would get.
More likely, they just haven't cut accounts payable checks for the month yet. While 3 weeks is understandably a long time for you, for most vendors expecting a check it's not. In many companies the process of submitting a reimbursement request and having a check issued is tedious.
Send a polite email, asking when you can expect to receive your reimbursement. Then try to be patient and not worry until it's warranted.