First of all, could I ask who advised you to trim the hair of the dog? Whosoever advised you this is either a fool ( excuse me ) or has no knowledge in dog care. The first thing you need to know is, during Summers, dog loose their upper coat so that the softer inner coat can trap air to keep their body cool. Trimming hair would mean playing havoc with this natural process. Secondly, by trimming the hair you have only made your problem even worse. Long hair can still be easily picked. Short hair can become very stubborn and can cause discomfort. If they are in your bed/clothes, they can cause you a lot of discomfort.
Shedding is a very natural process. You can control this problem by regularly grooming your dog. What you need is a good deshedding brush and apply it all over his body. If you are doing it for the first time, I'd advise you to do this out of the house as your dog will shed a lot of fur on the first occasion. You should repeat the grooming daily for 5-10 minutes. This will ensure, atleast dead hair are properly removed off the body and disposed off, resulting in less number of hair on your floor. You can also order the brush on this website. Their service is excellent and they also offer cash on delivery service. Check this out : https://www.dogspot.in/shop/ca tegory/shedding-control
Also, read this important article on grooming Labrador :https://www.woodhavenlabs.com /grooming.html.
Secondly, I'd also suggest you to give a good skin supplement to your dog. Nutricoat is good and easily available.
Your problem of ticks can also be reduced, if you daily groom your dog. If you think your dog is heavily infected with ticks, you can use a good anti-tick shampoo. There are some very good brands available in this site. https://www.dogspot.in/shop/ca tegory/flea-ticks.
The best products in my experience are Frontline ( expensive but very effective ), Kiltick Collar ( can be used for 6 months and not very expensive )and Advantix ( again, an excellent product which doesn't just kill the existing ticks but also works as a repellent for ticks as well as mosquitoes.
Also, don't let your dog play in grass or filthy place as the dogs are most likely to catch ticks and fleas from there.