Not to worry.
If it was a tick then you MAY get a very typical rash.
Not all ticks carry nasties.
You have done theright thing and been to Dr. But if ever you get another tick/? then try to catch the thing in a jar with lid so it can be identified. And also wipe the place over with antibiotic (Dettol or TCP or whatever).
Dr. may give you aparticular antibiotic for a month or he may wait to see if rash develops first..
A homeopath will advise you with any tick bite to take Ledum immediately but if you are not into homeopathy then you have no option but to trust the GP.
Ledum is the wild rosemary. It cannot harm in any way.
If your cat/dog ever gets bitten by a tick give it Ledum straight away.
Cat's brown ball certainly sounds suspicious.(back bit of a tick)cats and dogs often get Lyme but seem to throw it off more easily than humans.
My grandchild then 6 returned from trip in Devon with a tick embedded.Daughter just removed it with a tickstick. Did not take her to Dr or wipe it with antibiotic.
She seems ok. (a year later).
More people have Lyme than is realised and it is misdiagnosed. and because they have strong immune systems they seem to cope with it.
If all dogs were tested then probably it would be found many had Lyme.
Do not start to worry until you need to. There is plenty of time for antibiotics to cure you completely.
Always wear clothing that covers you, long trousers and long sleeved tops/shirts and spray anti tick stuff on before you go into woodland or areas where there might be ticks., even your garden.
Ticks seem to be on the increase.
Meanwhile boost your immune system, plenty vit C and a good diet.
Let us know how you get on.
Hopefully all will be well.
PS If cat seems to be affected in any way take it to vet. Vet can give it antibiotics and later do a test.
First Doctor was acting as normal. GP's seem to have some sort of Ministry of health protocol when handing out antibiotics.
Second Dr was acting as a GP should and allaying your fears by offering you a follow up appointment.
Try to stay calm as otherwise they label you as suffering from depression which is unhelpful in this situation.
Remember not all ticks carry these particular bacteria that cause Lyme.
We are constantly being bitten when in the garden and the bites swell and itch but not all are tick bites.
You are not neurotic just over -anxious- as most intelligent and sensitive people are.