I was kept driving yesterday.
This sentence is in the Passive Voice: be + past participle (kept). The meaning is: someone or something kept me driving yesterday. The sentence looks a bit unnatural, but seems to be grammatical.
You can remodel this sentence to the Active Voice in a way that will change its meaning:
I kept driving yesterday. (I continued to drive yesterday; by myself - no mention of someone or somebody "forcing" me to drive)
Your second sentence is incorrect:
I was keep driving yesterday.
You cannot use the basic form of the verb ("keep") after "was", you've got to pick either "kept" (past participle) or "keeping" (present participle). We combine be with other verbs to form progressive constructions:
I was writing a reply at Stack Exchange. (be + verb[ing])
and passive voice constructions:
I was given 10 points for my reply at Stack Exchange. (be + past participle)
P.S. The "Keeping driving" combination would look strange though.