Teenylee, you don't need to move. You just need to lock your doors and additionally, add things like upright "door jams."
If the problem with an alarm system is that you rent, most landlords will be cool with chain-locks, and you usually have the right to change locks so long as you give the landlord a key.
Of course none of these things solved my problem last year, as it was our landlord who unlocked and let himself in, without notice, while I was still sleeping in my underwear and tiny t-shirt. But door jams at least afforded me the security of taking a brief shower or whatever when I was in the house alone.
And except for in difficult situation like the one above, there is really no reason for someone to be walking into your place! Lock, maybe add a little extra, and ignore this guy.