Is she cheating on me?

I have been married for 35 years, I have just found out my wife has been texting, calling a man who is her patient.

It started about 8 months ago, there are hundreds of texts every month, mostly he is seeking medical advise for himself or some one in his family, but also I found out she has been showering him with expensive gifts, and she has accepted a birthday gift from him.

Some background,My wife is in her mid fifties a medical doctor , all the children out of the house or away in college, he is 50 years old not a good looking guy , I don't believe he is educated , he was in construction and got injured and know he is on long term disability.

When I asked about kind of friend is he, she state that he is just a patient who has some sort of disability and she saved his life once.

She did say that a few weeks ago he wanted to move the friendship or the relationship to the next level and she refused, however, she still communicates with him and refused to ended.

I am not really looking for a divorce , but , I can't get this out of my mind ,
Please help , is she cheating????

Should I end the marriage?

I am not sure if they had sex , but, she admits they kissed and went out for drinks few times which I find very strange becuse my wife is shy and people will recognize her in town ,she never stayed out all night, but , she came very late few times and said she was in the office working.

Some times I smell smoke on her even though She doesn't smoke,