Can I still wear my retainer with front teeth crowns?

You can try in your retainer. Chances are that it will no longer fit. If this is the case you really need to have a new retainer made. Depending on the type of retainer you have, your dentist may be able to adjust the fit to accommodate your new crowns. If you do nothing your teeth will continue to move.

It is possible that your old retainer would not fit because you had some work done on your front teeth. 

Unfortunately, your old retainer was designed around the existing teeth at that time.  Since new crowns altered the shape (even if ever so slightly) a new retainer may be required if the old one can not be adjusted by your dentist or orthodontist.  Bring it in when you see your dentist, and don't wait since you noted that you are starting to feel shifting of your teeth.

Yes, you most certainly need to continue wearing your retainer to keep the teeth in alignment. Did your dentist check the fit of the retainer after the new crowns were placed?Most likely you will need to see your orthodontist to adjust the retainer or possibly even to make you a new one so that the retainer fits properly with your new crowns.

A retainer can be worn over crowns. However, the retainer will probably not fit since the crowns have been made and the teeth are a different size. What needs to be done is to have a new retainer made that will hold the teeth in place and fit with your new crowns.