Singleton httpClient to single Instance of AppService

First of all sorry for my horrible English :'(.

I'm developing a client to send POST messages to a WebAPI hosted in an Azure AppService. I read the best practicee is use the singleton pattern, so I developed in this way.

public static class UtilHTTP {

    private static readonly ConcurrentDictionary<string, HttpClient> dicClient = new ConcurrentDictionary<string, HttpClient>();

    public static string PostSingleton(string url, string contentType, string accept, string rq, Dictionary<string, string> headers)
    {
        Task<string> response = Fetch(url, contentType, accept, rq, headers);
        response.Wait();
        return response.Result;
    }

    private static HttpClient GetdicClient(string url, string contentType, string accept)
    {
        string key = string.Format("{0}#{1}#{2}", url, contentType, accept);
        if (!dicClient.ContainsKey(key))
        {
            dicClient.GetOrAdd(key, new HttpClient());

            if (!string.IsNullOrEmpty(accept))
            {
                dicClient[key].DefaultRequestHeaders.Accept.Add(new System.Net.Http.Headers.MediaTypeWithQualityHeaderValue(accept));
            }
        }
        return dicClient[key];
    }

    private static async Task<string> Fetch(string url, string contentType, string accept, string rq, Dictionary<string, string> headers)
    {
        //_http.Timeout = new TimeSpan(0,0,6);
        HttpContent content;
        if (string.IsNullOrEmpty(contentType))
        {
            content = new StringContent(rq, Encoding.UTF8);
        }
        else
        {
            content = new StringContent(rq, Encoding.UTF8, contentType);
        }

        if (headers != null)
        {
            foreach (KeyValuePair<string, string> h in headers)
            {
                content.Headers.Add(h.Key, h.Value);
            }
        }

        HttpResponseMessage response = await GetdicClient(url, contentType, accept).PostAsync(url, content);
        string resultContent = await response.Content.ReadAsStringAsync();

        if (!response.IsSuccessStatusCode)
        {
            resultContent = response.ReasonPhrase;
        }

        return resultContent;
    }

}

I have two instances of the service in the AppService, but all the requests are going to the same instance, so I can't scalate the service and the performance isn't really good.

Insights Performance

Is it something wrong in the code? Do you think is a problem in the Server side? Must I use another pattern?

Thank you very much!