That sounds like a confidence issue and hopefully with a bit of preparation and experience your confidence will improve.
There's a few areas that you could try with.
First of all, have you had any cycle training like Bikeability? Getting out with an instructor and being coached through the bits of road cycling you feel are dangerous can help massively. Also there are some good tips in the commuting section on this thread -
'Essential Guide for new commuter's', or there's the very good book Cyclecraft which would help.
For building up your confidence with the bike itself then try plotting out some nice low traffic routes online. Find your home on
bikehike or similar, and start designing routes down little yellow roads as much as possible if you can, away from the high traffic/speed roads. If you can find a group of people to ride with then even better as then you will be able to take confidence from them.
Of course there's also things you can do with the bike. If you are struggling to see over your shoulder then something like a bike eye mirror may help (if this is a point you are struggling with, then before spending money on kit, get out onto an empty car park and practice this over and over again where there's no hazards or vehicles about).
Also it is possible to fit cross-top levers on drop bars so you can have a much more upright riding position if that feels safer.
Hopefully somewhere in that lot there's something which could help