First and foremost, you can apply for the HC1 form which is the NHS's Low Income scheme which subsidises partially or fully the cost of dental treatment for those on low incomes. Once you have this sorted, see your dentist.
You say you have "black holes" - do you mean this literally or do you mean you have large gaps spatially between your teeth? If it's the former, then I'd advise you strongly to see your dentist as soon as possible as it could be tooth decay which needs to be treated before it progresses into a larger problem.
Do not try teeth whitening as someone poorly advised above - this will make your teeth even more sensitive.
Your asthma is unrelated to your tooth sensitivity.
Whilst it's great that you refrain from fizzy drinks and brush your teeth, you need to get detailed and personalised oral hygiene instruction from your dentist - they can identify what you're doing well and pinpoint areas of improvement.