All of them showed my current situation perfectly,looks like they were designed for me specially.

looks单数形式提示前面省略了and it或which。完整的句子应该是：

All of them showed my current situation perfectly,and it looks like they were designed for me specially.

或者：All of them showed my current situation perfectly, which looks like they were designed for me specially.

Like用作连词是非正式用法，此处=as if/as rhough

没有哪本语法书或词典说可以这样省略。但如果句子没有抄错的话，我们就看到了这样的句子。这显然是口语体，不规范的英语。见过了，有个印象就行了。不值得模仿使用。

补充内容

如果大家查词典并注意词典例句，就会发现look like/as if结构有两种用法。

第一，相当于seem的用法，主语为非人称代词it（虚指it），这时从句的谓语多为为一般将来时态。意为看目前情况某事有可能发生（还没有发生）或有可能是真实的。如：It looks like they won’t be needing us anymore.

第二，主语可以是名词或人称代词，包括人称代词it，这时从句谓语多为过去时态或现在完成时。意为主语显示出某种表象。如：He looked as if he hadn’t washed for a week.

本句中，like后从句用过去时，因此，looks的主语可以是人称代词it。It指代主句的内容，改为非限制定语从句时则用关系代词which取代it。这是完全可以的。

以下为引自COCA语料库的例句：

 But I think they will find the experts that will say that despite all of those actions, which looks like someone does know the difference between right and wrong, there are a lot of other things that someone will look at to say this woman, obviously, has mental health issues.

The knights will perform canter pirouettes. They'll perform half-passes, which looks like they're going -- well, they go sideways.

 "I will go to my grave regretting the photograph of me in an anti-aircraft carrier, which looks like I was trying to shoot at American planes, " Fonda told O, The Oprah Magazine.

And now we've got through McNulty and the others possibly a gotcha of a video of someone coming out of the back of a tank, which looks like they're firing into the compound. 

以上例句中which的先行词有的是主句内容，有的是主句的一部分。