Is everything random, or are at least some things logical? You can say this in everyday life language, which is a language that doesn't need to be exact, precise. But, if you want to talk in a proper philosophical way, what you said is a contradiction: "objective" , in a rigorous philosophical way, means absolutely independent from anybody. So, if you instead make it relative by adding "for me", it becomes contradictory. It is like saying "in my opinion this fact is independent from my opinion"; in everyday language this can be accepted, but philosophically it becomes meaningless or contradictory. Being able to build a sentence that is grammatically correct doesn't automatically guarantee that the sentence makes sense or has a meaning.
If a fact is really objective, you must be able to say "This is not my opinion, this is a fact". You can say "In my opinion this is not my opinion", but this is not philosophy, this is careless common language. Absolute objectivity is what Descartes tried to find: his effort was to find something about which you can say "This is not my opinion and I don't even say that I think that it is not my opinion; this is just a fact, undeniable for everybody". This is the true absolute objectivity that Descartes wanted to reach and this is what we mean when we say "objective" in a philosophical sense. A philosopher would never say "I think that this is objective".
Something similar can be found in everyday language when we say "Two plus two are four". It is not easy to find people saying "In my opinion 2+2=4". Normally they claim that it is not their opinion, it is just a fact, so that, in that case, adding "in my opinion" doesn't make sense even in everyday language.