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It is possible that in the next day or two the tight feeling will ease and you will be able to get floss through the contact between your teeth. It may be possible for the dentist to use fine polishing tape to ease the contact pressure.
If you are uncomfortable, it will be best to discuss this with your dentist. I am sure that he /she will want you to be happy and consider remaking the crown for you.

It sounds like there was a discrepancy with the impression when it was taken or you did not have a well made temporary crown in your mouth while the crown was being made so the surrounding teeth may have moved into the space of your new crown.

Either way any unbalanced force in your mouth is unpredictable and bad long term and it is often hard to work out the pressure when you are numb.A certain amount of minimal trimming is needed to eliminate any unbalanced forces in your mouth . Not allowing floss to get down is not good for your long term oral health as I am sure you realise , this adjustment should have been done before it was cemented and very hard to adjust well after it is cemented to polish it well .

To keep a successful practice sustainable with a receptionist and staff, requires a dentist to earn about at least £ 200 per hour .(depending on the technology and materials used )

Their time needs to be carefully measured so if your crown was cheap ,then they cannot spend the time required to ensure it is the best it can be . It does sound like he/she has behaved responsibly by offering to adjust the  discomfort for you.

Do not accept anything that is pushing longterm or causes sensitivity at all . This can cause long term damage that may cost you a lot in the long run.

Each tooth sits on a fibrous tissue ligament within the jaw bone and is able to "bounce" when chewed on and can drift position if the forces on it change (such as when a brace is worn or the opposing tooth is lost) Depending on the type and size of temporary crown placed it is possible that contact has not been maintained between this tooth and its neighbours. Especially if your dentist just placed a lump of temporary filling to cover the prepared tooth.
Hopefully over the next couple of weeks the teeth will shuffle back to their original position to accept this new crown and all will be well
However if you find that a month has passed with no improvement or the bite is affected then you will need to have the crown adjusted but this can leas to problems as they are difficult to re-polish in the mouth