Bunions are bony lumps on the side of your feet, caused by pressure on the toe joint which then forces your toes together.
Although bunions can only be removed with surgery there are ways to reduce the effects of having them. General recommendations are to do things like wear bunion pads to prevent rubbing, wear wide shoes and use ice to reduce the swelling around it. However, it is suggested that improper footwear can lead to the development of bunions and so may be one of the best ways to limit the effects of them.
Seeing a podiatrist can help find shoes that fit you properly and also support you in the correct places to prevent loading the joint and worsening the problem. Some studies have also noted that exercises such as ‘Short Foot’, ‘Toe Spread’ and ‘Heel Raise’ can strengthen 5 key muscles to reduce unnecessary loading on the toe joint.
So short answer is yes you can run with bunions. There are wider shoes available but you may need to seek help in choosing something to fit your foot. Look into those exercises and avoid pointy shoes that compress your feet and toes.