What do you really want to do???? That is by no means clear: If you do an integral

Integrate[ .... , { x, a, b } ]

you get a single number - if you are lucky. Here this would not work, because your integrand has a singularity for x == 3.2445 !

And in addition: how could one plot a single number? You are supposed to have a function of something.

I try to guess what you perhaps mean.

I define a function which resemble yours (but I am not sure if you meant this)

f[x_, low_] := 
 NIntegrate[NIntegrate[Exp[(z - 3.2446)^(1/4)], {z, low, x}]/Sqrt[(y - 3.2445)^(1/2)], {y, low, x}]

Left of the singularity you get complex numbers

In[37]:= f[3, -10]
Out[37]= 321.353 + 115.379 I

But in the positive region and above the singularity you can get a plot:

Plot[f[x, 3.3], {x, 3.3, 10}]