Will it be in sun or shade? One of the small azaleas might do the trick if its not too sunny (they need acid soil, ie ericaceous compost) Check before buying though as many of them get larger. Nothing evergreen and flowering that I can think of will stay narrow when it gets taller though.
Had you thought of having two containers, one for winter and one for summer? That would make flowers a lot easier.

I've got a Camelia in one pot and another in a trough about 14 inches deep. They have been growing and flowering for years. They are pruned occasionally to keep them from getting too big.

I like skimmia as there is a self fertile one that means evergreen foliage, attractive buds, fragrant flowers in spring and berries in the autumn. they can take a lot of 'abuse' if conditions aren't perfect in the ground or a pot. mine are in semi shade but the neighbour's is in full sun on poor soil and it never fails to perform.

welcome to GoY too.

Reevesiana or Temptation are self fertile ones. But they won't give you summer flowers if thats what you are after.

Sarcococca, Sweet Box would be my choice. Evergreen, lots of sweetly-scented small, white flowers around Christmas time with black or purple berries to follow. Will be especially appreciated when grown in a pot which is situated near the house or walkway. Quite a few varieties; purple stem worth looking at.

Dull in summer though and dislikes a lot of sun - hence suggestion to have two lots of pots?

Nandina domestica or Euonymus alatus.