You can't unblock on your own from somebody else's profile unless you have access to that account yourself.
How To Make Someone Unblock You On Facebook
However, there are a few points that might make you really feel better:
: > You can still view whatever they publish openly (as long as you aren't viewing it as/from the blocked account). You simply will not see what they upload to good friends.
: > You can still see their public profile by visiting it's unique LINK (www.facebook.com/firstname.lastname, generally).
: > You can make a brand-new account and also with any luck add the individual who blocked you to this brand-new account (making believe to be somebody else). Nonetheless, I watch this as a last option and also do not suggest it since it can backfire as well as make things worse than originally. This is against Facebook's TOS, also.
: > If you understand their Facebook email address, you can write them an e-mail from a routine email account and it might most likely to their Facebook inbox (I think this still works).
: > There are various other ways to get in touch with the person (text, email, smoke signals/pigeons, and so on).
In addition to those things, you can ask them to unblock you. If they do not, feel far better recognizing the individual who blocked you doesn't care anymore (if they apparently never cared, really feel even better).
Do not seem like you can't get a message to this person, since you can if you really intend to.