I don't understand what you are asking.
There are about seven approved levothyroxine formulations in the USA.
Some are repackaged under other names (e.g. Kaiser).
Each formulation is different.
Typically people in the USA seem to claim that Synthroid is THE brand and everything else is a generic. This does not take account of the fact that when required to get levothyroxine products approved, Synthroid were well down the list. So actually Unithroid was the first approved levothyroxine product. Although obscured by all sorts of other factors, the usual idea is that every other formulation has to be shown to match the first approved product.
Nor does it take account of the fact that products such as Levoxyl and Unithroid are themselves brands. Nor that levothyroxine was never patented in the USA. So the conventional "original patented brand" versus "later generic versions when patent ran out" distinction simply does not apply.
This FDA paper might be of some interest:
It is not at all surprising if someone is intolerant of one or more formulations but fine on others. That is well known and widespread experience.