Roof insurance claim advice

[Anita Ainsworth]

Hi, apologises if this is the wrong forum to request advice on insurance claims. Following the recent storms in the US my Davenport property sustained roof, window and interior water damage.  I contacted the insurance company and was sent a cheque for a 1/3rd of the repair estimate . I believed I paid for the best premium available on offer, nearly $4000 per annum so was extremely disappointed by the offer. My question,  if I don’t pay in the cheque but pay for the work to be done privately would this still be classed as an insurance claim? Sorry may seem an oblivious question to most but due to being based in UK and having communication probs with insurance co. I thought I would seek independent advice. 
Also advice would be welcomed on the cost of replacing a shingle roof measuring 53ft x 58ft completed by  a reliable trustworthy roofer permitted to carry out work in Florida. 
thank you very much.