Mostly we consider 'to have' as a stative verb so we say 'I have a lot of tests.'
However, there are plenty of occasions where we would use the continuous form.
"I'm having a lot of tests lately! It's awful!"
"Doctor, I'm having a lot of headaches. Is there something wrong with me?"
"I'm having a fantastic holiday!"
Also, in Indian English, which is a perfectly valid form of English spoken by hundreds of millions, the use of the continuous form is very acceptable, in almost all cases. "I'm having a headache today, I think I need to rest."
For many of us that would sound funny - like it's booked in the diary for later that day.
We need to WATCH THIS SPACE, as they say. English is evolving rapidly and the grammar books are gradually catching up.
For my exam students I would advise caution on the use of TO HAVE. Use it in the stative unless you are sure it works well in the continuous.