"I just have two shirts."

It would be correct

Tengo solamente dos camisas was wrong also?

That sentence is wrong in Spanish. You use "unico/a" as an adjective, it modifies the noun and means is the only one. So if you have two, it isn't unica. You might use the plural (unicas) but it would be before "camisas" since that's the noun the adjective qualifies, as in "tengo dos unicas camisas", and still isn't natural nor it means "just two shirts"; it would translate "I just/only have these two shirts"