Question

Is this sentence right?
"Me too!"
Or it should be written as "I too!"

Answer 1

Technically it's "I too" because it's a contraction of "I do, too."
Although "Me too" has become widely accepted, so I doubt anything would be marked off by using it.

Answer 2

It sort of depends.

In the case of, “Me too has given you a present,” you should probably use ‘I’ instead of ‘Me’.

If you are talking about ‘I too’ and ‘Me too’ as independent sentences, both are acceptable.