Can homeopathy cure chronic anxiety allergies and asthma, been seeing my homeopath for four months now, still no better?

Chronic? Yes, homeopathy can help you cure these problems, assuming there are no obstacles to cure. With a well-taken case and accurately prescribed remedy, there should be a sense of forward progress within a few weeks -- even if not all symptoms are yet "gone." full healing may require a year or more, from your list of problems (esp the anxiety). Develop clear goals and keep track. [see comment].
Chronic problems. ...Take longer then 4 months, however, you should communicate with your practitioner express your doubts, and review your treatment plan. I would like to see anxiety level improve first, then asthma, and lastly allergies as your progression to health.
Yes, however... Cure is a strong word but homeopathy has the potential to help and at times actually cure these conditions. This takes time but i'd expect signs of progress if you were on the optimal remedy. The challenge is that there are over 3000 remedies used in homeopathy and only 1might cure you(though a few might help to lesser degrees). Even the best homeopath doesn't get it right every time. See comment:.