Is it necessary to go to immigration for my 3-month stamp in May while on lockdown in Patong?

if you are indeed in Phuket (which Patong is a part) you need to call the Phuket immigration office directly. They should be able to tell you what to do,

IF I was to guess, I'd say because you're on a 'long term' extension you are NOT covered on the amnesty program and you're gonna hafta get the documents from your school saying you're still studying so you can extend your stamp OR that you are no longer studying so you can cancel your current extension and then you would be covered by the amnesty.

You are not covered by the amnesty extension to July 31.

Then you need to get the documents from your school and go apply for the extension like normal.

How about we start with what extension you're on and what you mean by your "3 month stamp".