Can this sentence also mean that my whole life I've been looking for a partner?
I believe that would be "אני מחפשת לבן זוג במשך כל החיים". Any native Hebrew speakers who can confirm that? Is there a better way to say it?
(Diclaimer: non-native opinion) Well, בְּמֶ֫שֶׁךְ כׇּל הַחַיִּם שֶׁלִּי sounds fine, but often the בְּמֶ֫שֶׁךְ is left out, forming an adverbial accusative: יֵשׁ טָעֻיּוֹת שֶׁמְּשַׁלְּמִים עֲלֵיהֶן כׇּל הַחַיִּים There are mistakes one has to pay for life. This is already old biblical usage: ועפר תאכל כל ימי חייך Gen 3.14 and you will eat dust all the days of your life.
I believe "I am searching for a partner for all of life." should be acceptable.