I'm suffering from peptic ulcer; Are there any cough products I can take that will not make it worse

Yes there are many cough medicines that you can safely take whilst you have an ulcer - talk with your pharmacist. You will need to be questioned about the type of cough you have (productive or non-productive) how long you have had it for etc.
You need to look out for any medicines containing nonsteroidal anti-inflammatory drugs (NSAIDs)—such as aspirin and ibuprofen as these can make your ulcer worse.
There are many cough medicines available over the counter that do not contain these ingredients.