You do not get HIV from shaking hands with someone, bandages or not.
C,
I think you know the answer to your question. In case you don't, here it is: there is no chance, not one in a million, one in a billion or one in a trillion, that you acquired HIV from the scenario that you described. No way, no how, it just doesn't happen this way, has never happened this way and NEVER will happen this way.
I also think you know what is driving you to be worried about this situation: HIV phobia (you said it yourself). You said that you had, at one time, had a risky encounter. Without knowing the details of that encounter, hard for me to say how risky it truly was. But what I do know is this: if you are predisposed to worry about things like this, many, many things that really aren't very risky can be very scary indeed.
Any phobia can come and go on its own, or last a lifetime. You can be born with a predisposition to general phobic behavior, or you can develop specific phobias based on events in your life. Whichever category you fall into, it is important to recognize when a certain phobia is interfering with you ability to lead a happy and fulfilling life. A simple fear of spiders is one thing, being afraid to touch anyone, or to engage in intimacy, is quite another.
If you feel that you fall into the latter category, you may want to consider getting professional help. And that's not a knock on you - plenty of people suffer from irrational fears, and it can take a certain amount of guts to admit that you both need help in getting over them, and then seeking out and getting that help.
Now, of course, not sure that you fall into this category. If not, ignore me, I'm used to it ;-). But, if you think you might, and you haven't done so already, you might consider making an appointment with a therapist. The good news is that most phobias and OCD related issues (such as hypochondria - not saying you suffer from this, just throwing it out there as an FYI) are readily treatable.
So, just to summarize, no, there was absolutely no risk of contracting HIV in the encounter that you described. So, put that thought right out of your mind.
Take care.