I recently declined a really good PhD offer in the US for another offer from an American university and I'm terribly regretting it now.
I made my decision on the 15th of April and it's past deadline now. I really want to go to the other school and since the 15th of April was the last working day, I'm hoping that they haven't offered my position to any other aspirant yet. I know this is ethically wrong but I feel miserable about my decision and want to contact the university and ask them if they can still accommodate me.
As far as the other university is concerned I have only accepted their offer through an email and haven't formally been given the final offer letter yet. Should I go ahead with this?
I don't have much experience of US PhD programs, but in the UK it would be quite likely that the place you declined would have been offered to the next candidate almost immediately after you declined it. Again from a UK perspective, it would also give a somewhat unfavorable impression that you declined and then changed your mind. A potential worry for the University making the offer would be that you might change your mind again at a later point.
You don't mention your reasons for declining the offer the first time, I would reflect on these before doing anything further or in haste.
Having said all that, if after reflection you still feel that it was a mistake to decline the offer, I would suggest informally contacting the University where you declined the offer and asking if there is any possibility for you to change your mind. If you don't ask, you'll never know.